AP Stats Final

The number of tickets purchased by a customer for a musical performance at a certain concert hall can be considered a random variable. The table below shows the relative frequency distribution for the number of tickets purchased by a customer. Suppose each ticket for a certain musical performance cost $12. Based on the distribution shown, what is the mean cost per customer for the performance?

$29.40

A company sells concrete in batches of 5 cubic yards. The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table below. The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76. There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by Y = 75X - 100. What is the standard deviation of Y?

$432.00

The marketing director for an ice cream company investigated whether there was a difference in preference for two new ice cream flavors—cotton candy and mango. Each participant from a large group of people was randomly assigned to taste one of the two flavors. After tasting, each person rated the flavor on a numerical scale from 1 to 5, where 1 represented strongly dislike and 5 represented strongly like. A two-sample t-interval for a difference between means (cotton candy minus mango) was constructed. Based on the interval, there was convincing statistical evidence of a difference in population mean flavor ratings, with mango having the greater sample mean rating. Which of the following could be the constructed interval?

( -2.1, -1.3 )

There are 1,000 golden delicious and 1,000 red delicious apples in a cooler. In a random sample of 75 of the golden delicious apples, 48 had blemishes. In a random sample of 75 of the red delicious apples, 42 had blemishes. Assume all conditions for inference have been met. Which of the following is closest to the interval estimate of the difference in the numbers of apples with blemishes (golden delicious minus red delicious) at a 98 percent level of confidence?

(-105,265)

According to a recent survey, 31 percent of the residents of a certain state who are age 25 years or older have a bachelor's degree. A random sample of 50 residents of the state, age 25 years or older, will be selected. Let the random variable B represent the number in the sample who have a bachelor's degree. What is the probability that B will equal 40 ?

(4050​)(0.31)40(0.69)10

Researchers are studying populations of two squirrels, the eastern gray and the western gray. For the eastern gray squirrel, about 22 percent of the population weighs over 0.5 kilogram (kg). For the western gray squirrel, about 36 percent of the population weighs over 0.5 kg. A random sample of 60 squirrels will be selected from the population of eastern gray squirrels, and a random sample of 120 squirrels will be selected from the population of western gray squirrels. What is the mean of the sampling distribution of the difference in sample proportions (eastern minus western)

(E) 0.22 - 0.36

Suppose that 25 percent of women and 22 percent of men would answer yes to a particular question. In a simulation, a random sample of 100 women and a random sample of 100 men were selected, and the difference in sample proportions of those who answered yes, p̂women - p̂men, was calculated. The process was repeated 1,000 times. Which of the following is most likely to be a representation of the simulated sampling distribution of the difference between the two sample proportions?

-.20 to .20

Carly commutes to work, and her commute time is dependent on the weather. When the weather is good, the distribution of her commute times is approximately normal with mean 20 minutes and standard deviation 2 minutes. When the weather is not good, the distribution of her commute times is approximately normal with mean 30 minutes and standard deviation 4 minutes. Suppose the probability that the weather will be good tomorrow is 0.9. Which of the following is closest to the probability that Carly's commute time tomorrow will be greater than 25 minutes?

0.0950 C

At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. Which of the following is closest to the proportion of orders that are processed in less than 240 seconds?

0.17

Of all the fish in a certain river, 20 percent are salmon. Once a year, people can purchase a fishing license that allows them to catch up to 8 fish. Assume each catch is independent. Which of the following represents the probability of needing to catch 8 fish to get the first salmon?

0.2(0.8)7

Researchers are studying populations of two squirrels, the eastern gray and the western gray. For the eastern gray squirrel, about 22 percent of the population weighs over 0.5 kilogram (kg)(kg). For the western gray squirrel, about 36 percent of the population weighs over 0.5 kgkg. A random sample of 60 squirrels will be selected from the population of eastern gray squirrels, and a random sample of 120 squirrels will be selected from the population of western gray squirrels. What is the mean of the sampling distribution of the difference in sample proportions (eastern minus western) ?

0.22−0.36

A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. The reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. Suppose the reported values are the true mean and standard deviation for the population of subjects in the study. If a random sample of 144 subjects is selected from the population, what is the approximate probability that the mean of the sample will be more than 11.0 seconds?

0.2743

A recent survey concluded that the proportion of American teenagers who have a cell phone is 0.27. The true population proportion of American teenagers who have a cell phone is 0.29. For samples of size 1,000 that are selected at random from this population, what are the mean and standard deviation, respectively, for the sampling distribution of the sample proportion of American teenagers who have a cell phone?

0.29,1000(0.29)(0.71)​

A recent survey concluded that the proportion of American teenagers who have a cell phone is 0.27. The true population proportion of American teenagers who have a cell phone is 0.29. For samples of size 1,000 that are selected at random from this population, what are the mean and standard deviation, respectively, for the sampling distribution of the sample proportion of American teenagers who have a cell phone?

0.29,1000(0.29)(0.71)​​

Based on his past record, Luke, an archer for a college archery team, has a probability of 0.90 of hitting the inner ring of the target with a shot of the arrow. Assume that in one practice Luke will attempt 5 shots of the arrow and that each shot is independent from the others. Let the random variable X represent the number of times he hits the inner ring of the target in 5 attempts. The probability distribution of X is given in the table. What is the probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X ?

0.40951

The transaction history at an electronic goods store indicates that 21 percent of customers purchase the extended warranty when they buy an eligible item. Suppose customers who buy eligible items are chosen at random, one at a time, until one is found who purchased the extended warranty. Let the random variable X represent the number of customers it takes to find one who purchased the extended warranty. Assume customers' decisions on whether to purchase the extended warranty are independent. Which of the following is closest to the probability that X > 3; that is, the probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty?

0.493

A restaurant manager collected data to predict monthly sales for the restaurant from monthly advertising expenses. The model created from the data showed that 36 percent of the variation in monthly sales could be explained by monthly advertising expenses. What was the value of the correlation coefficient?

0.60

The following question(s) refer to the following scenario and set of data. In the 1830s, land surveyors began to survey the land acquired in the Louisiana Purchase. Part of their task was to note the sizes of trees they encountered in their surveying. The table of data below is for bur oak trees measured during the survey. Which of the following differences in cumulative relative frequencies gives the proportion of trees that are 12 inches to 16 inches, inclusive, in diameter?

0.726-0.325

The least-squares regression line yˆ=1.8−0.2xy^⁢=1.8−0.2x summarizes the relationship between velocity, in feet per second, and depth, in feet, in measurements taken for a certain river, where xx represents velocity and yy represents the depth of the river. What is the predicted value of yy, in feet, when x=5x=5?

0.8

The table shows several values of xx and their corresponding values of yy. Which of the following is closest to the correlation between xx and yy?

0.98

Clara recorded 50 numerical observations on a certain variable and then calculated the mean \overline{x}x and the standard deviation s for the observations. To help decide whether a normal model is appropriate, she created the following chart. In Clara's chart, the letters a, b, c, d, and e represent the number of observations falling in each interval. Which of the following list of counts for a, b, c, d, and e respectively, is the best indicator that the variable can be modeled with a normal approximation?

1, 7, 34, 7, 1

Clara recorded 50 numerical observations on a certain variable and then calculated the mean x‾x and the standard deviation s for the observations. To help decide whether a normal model is appropriate, she created the following chart. In Clara's chart, the letters a, b, c, d, and e represent the number of observations falling in each interval. Which of the following list of counts for a, b, c, d, and e respectively, is the best indicator that the variable can be modeled with a normal approximation?

1, 7, 34, 7, 1

For a certain dog breed, the number of puppies in a litter typically varies from 2 to 6. The following table shows the probability distribution of the random variable N, where N represents the number of puppies in a litter. Also shown are the squared deviations, or distances, from the expected value of 4.5 for the distribution. Number of puppies23456Squared deviation6.252.250.250.252.25Probability0.050.150.250.350.20 What is the variance of the distribution?

1.25

At a certain bakery, the price of each doughnut is $1.50. Let the random variable D represent the number of doughnuts a typical customer purchases each day. The expected value and variance of the probability distribution of D are 2.6 doughnuts and 3.6(doughnuts)^2, respectively. Let the random variable P represent the price of the doughnuts that a typical customer purchases each day. Which of the following is the standard deviation, in dollars, of the probability distribution of P ?

1.5\sqrt{3.6}1.53.6​

Researchers are studying the distribution of subscribers to a certain streaming service in different populations. From a random sample of 200 people in City C, 34 were found to subscribe to the streaming service. From a random sample of 200 people in City K, 54 were found to subscribe to the streaming service. Assuming all conditions for inference are met, which of the following is a 90 percent confidence interval for the difference in population proportions (City C minus City K) who subscribe to the streaming service?

1.65 everything over 200

A company ships gift baskets that contain apples and pears. The distributions of weight for the apples, the pears, and the baskets are each approximately normal. The mean and standard deviation for each distribution is shown in the table below. The weights of the items are assumed to be independent. Let the random variable W represent the total weight of 4 apples, 6 pears, and 1 basket. Which of the following is closest to the standard deviation of W ?

1.97 ounces

Which of the following is the best estimate of the standard deviation of the distribution shown in the figure above? (30, 40, 50, 60, 70)

10

According to a survey about how workers get to work in Wyoming, 77 percent of workers get to work by driving alone, 11 percent get to work by carpooling, 4 percent get to work by walking, and 8 percent get to work by other means of transportation. Suppose a sample of 200 Wyoming workers is selected at random. Let the random variable D represent the number of workers in the sample who get to work by driving alone. What is the expected value of D?

154

Shalise competed in a jigsaw puzzle competition where participants are timed on how long they take to complete puzzles of various sizes. Shalise completed a small puzzle in 75 minutes and a large jigsaw puzzle in 140 minutes. For all participants, the distribution of completion time for the small puzzle was approximately normal with mean 60 minutes and standard deviation 15 minutes. The distribution of completion time for the large puzzle was approximately normal with mean 180 minutes and standard deviation 40 minutes. Approximately what percent of the participants had finishing times greater than Shalise's for each puzzle?

16% on the small puzzle and 84% on the large puzzle

There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least squares fit of some data collected by a biologist gives the model ŷ = 25.2 + 3.3x 9 < x < 25, where x is the number of chirps per minute and ŷ is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 5 chirps per minute?

16.5 ° F

A random variable X has a mean of 120 and a standard deviation of 15. A random variable Y has a mean of 100 and a standard deviation of 9. If X and Y are independent, approximately what is the standard deviation of X - Y ?

17.5

A carnival game allows the player a choice of simultaneously rolling two, four, six, eight, or ten fair dice. Each die has six faces numbered 1 through 6, respectively. After the player rolls the dice, the numbers that appear on the faces that land up are recorded. The player wins if the greatest number recorded is 1 or 2. How many dice should the player choose to roll to maximize the chance of winning?

2

A mathematics competition uses the following scoring procedure to discourage students from guessing (choosing an answer randomly) on the multiple-choice questions. For each correct response, the score is 7. For each question left unanswered, the score is 2. For each incorrect response, the score is 0. If there are 5 choices for each question, what is the minimum number of choices that the student must eliminate before it is advantageous to guess among the rest?

2

According to a recent survey, 47 percent of the people living in a certain region carry a certain genetic trait. People from the region will be selected at random one at a time until someone is found who carries the genetic trait. Let the random variable G represent the number of people selected to find one person who carries the genetic trait. On average, how many people from the region will need to be selected to find one person who carries the genetic trait?

2.13

A fair six-sided die, with sides numbered 1 through 6, will be rolled a total of 15 times. Let x¯1x¯1 represent the average of the first ten rolls, and let x¯2x¯2 represent the average of the remaining five rolls. What is the mean μ(x¯1−x¯2)μ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2x¯1−x¯2 ?

3.5−3.5=0

City R is a large city with 4 million residents, and City S is a smaller city with 0.25 million residents. Researchers believe that the proportion of City S residents who regularly ride bicycles is between 10 percent and 25 percent and the proportion of City R residents who regularly ride bicycles is between 20 percent and 50 percent. Suppose two independent random samples of residents from each city will be taken and the proportion of residents who ride bicycles is recorded. Based on the population proportions of residents who regularly ride bicycles, which of the following sample sizes is large enough to guarantee that the sampling distribution of the difference in sample proportions will be approximately normal?

50 in City R and 100 in City S

A certain monthly magazine has both print and online subscribers. Print subscribers are people who pay to have the magazine physically delivered to them each month. Online subscribers are people who pay to have access to the electronic version of the magazine. The editors of the magazine want to study how online subscribers feel about the design of the electronic version, and they will gather data from a sample. Which of the following is a sample of the population of interest?

50 online subscribers

Dairy farmers are aware there is often a linear relationship between the age, in years, of a dairy cow and the amount of milk produced, in gallons per week. The least-squares regression line produced from a random sample is Milkˆ=40.8−1.1(Age)Milk^=40.8−1.1(Age). Based on the model, what is the difference in predicted amounts of milk produced between a cow of 5 years and a cow of 10 years?

A cow of 5 years is predicted to produce 5.5 MORE GALLONS per week.

The following is a residual plot for a linear regression of yy versus xx. What is indicated by the plot?

A linear model is not appropriate.

A manufacturer claims its Brand A battery lasts longer than its competitor's Brand B battery. Nine batteries of each brand are tested independently, and the hours of battery life are shown in the table below. Provided that the assumptions for inference are met, which of the following tests should be conducted to determine if Brand A batteries do, in fact, last longer than Brand B batteries?

A one-sided, two-sample t-test

For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal?

A random sample of 10 taken from a population distribution that is skewed to the right

Researchers will conduct a study of the television-viewing habits of children. They will select a simple random sample of children and record the number of hours of television the children watch per week. The researchers will report the sample mean as a point estimate for the population mean. Which of the following statements is correct for the sample mean as a point estimator?

A sample of size 25 will produce more variability of the estimator than a sample of size 50.

Researchers will conduct a study of the television-viewing habits of children. They will select a simple random sample of children and record the number of hours of television the children watch per week. The researchers will report the sample mean as a point estimate for the population mean. Which of the following statements is correct for the sample mean as a point estimator? A sample of size 25 will produce less variability of the estimator than a sample of size 50.

A sample of size 25 will produce more variability of the estimator than a sample of size 50.

Researchers will conduct a study of the television-viewing habits of children. They will select a simple random sample of children and record the number of hours of television the children watch per week. The researchers will report the sample mean as a point estimate for the population mean. Which of the following statements is correct for the sample mean as a point estimator?

A sample of size 25 will produce more variability of the estimator than a sample of size 50. A

The weekly sales at two movie theaters were recorded for a random sample of 25 weeks. A 95 percent confidence interval for the difference in mean weekly sales for the two movie theaters was calculated as ( $1,288, $2,586 ) With all else remaining constant, which of the following would have resulted in a confidence interval narrower than the calculated interval?

A sample size greater than 25

A simulation was conducted using 10 fair six-sided dice, where the faces were numbered 1 through 6, respectively. All 10 dice were rolled, and the average of the 10 numbers appearing faceup was recorded. The process was repeated 20 times. Which of the following best describes the distribution being simulated?

A sampling distribution of a sample mean with n = 10, μx̄ = 3.5, and σx̄ ≈ 0.54

A simulation was conducted using 10 fair six-sided dice, where the faces were numbered 1 through 6, respectively. All 10 dice were rolled, and the average of the 10 numbers appearing faceup was recorded. The process was repeated 20 times. Which of the following best describes the distribution being simulated?

A sampling distribution of a sample mean with n = 10, μx̄ = 3.5, and σx̄ ≈ 0.54. A

A pollster is interested in comparing the proportions of women and men in a particular town who are in favor of a ban on fireworks within town borders. The pollster plans to test the hypothesis that the proportion of women in favor of the ban is different from the proportion of men in favor of the ban. There are 4,673 women and 4,502 men who live in the town. From a simple random sample of 40 women in the town, the pollster finds that 38 favor the ban. From an independent simple random sample of 50 men in the town, the pollster finds that 27 favor the ban. Which of the following statements is true about this situation?

A two-proportion z-test would not be valid for these data.

A researcher in sports equipment is investigating the design of racing swimsuits for women. The researcher selected a sample of 40 women swimmers from high school swim teams in the state and randomly assigned each swimmer to one of two groups: suit A or suit B. The women will wear the assigned suits for a certain race, and the mean swim times for each group will be recorded. The difference in the sample mean swim times will be calculated. Which of the following is the appropriate inference procedure for analyzing the results?

A two-sample t-interval for a difference between population means

A study was conducted to investigate whether the mean price of a dozen eggs was different for two different grocery stores, Store A and Store B, in a large city. A carton of one dozen eggs from each store was randomly selected for each of 35 weeks, for a total sample size of 35 cartons from each store. The mean price of the 35 cartons was recorded for each store. The difference in the mean carton price for the stores will be calculated. Which of the following is the appropriate test for the study?

A two-sample t-test for a difference between population means

A study will be conducted to investigate whether there is a difference in mean tail lengths between two populations of snow leopards. Random samples of leopards will be selected from both populations, and the mean sample tail length will be calculated for each sample. Which of the following is the appropriate test for the study?

A two-sample t-test for a difference between population means

Market researchers wanted to know whether the placement of a new product on a supermarket shelf significantly increases the percent of shoppers who will buy the product. At Supermarket X, a new product was placed on the top shelf, and at Supermarket Y, the product was placed one shelf below the top shelf. To observe buying habits, the researchers selected a random sample of 364 shoppers at X and another random sample of 327 shoppers at Y. Of the selected shoppers at X, 15 bought the product, and of the selected shoppers at Y, 19 bought the product. Which of the following is the most appropriate method for analyzing the results?

A two-sample z-test for a difference in population proportions

To investigate whether there is a significant difference between two regions of a state in the percent of voters who intend to vote for the incumbent governor in the next election, a polling agency interviewed 300 randomly selected voters from the north of the state and 400 randomly selected voters from the south of the state. Of those interviewed, 200 from the north and 325 from the south indicated they intended to vote for the incumbent governor in the next election. Which of the following is the most appropriate method for analyzing the results?

A two-sample z-test for a difference in population proportions

The histograms show the results of three simulations of a sampling distribution of a sample mean. For each simulation, 1,500 samples of size n were selected from the same population and the sample mean was recorded. The value of n was different for each of the three simulations.

A,C,B. A

A certain skin cream is 80 percent effective in curing a common rash. A random sample of 100 people with the rash will use the cream. Which of the following is the best description of the shape of the sampling distribution of the sample proportion of those who will be cured?

Approximately normal

There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?

Approximately normal with mean $206,274 and standard deviation $3,788

There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?

Approximately normal with mean $206,274 and standard deviation $3,788. A

At a certain restaurant, the distribution of wait times between ordering a meal and receiving the meal has mean 11.4 minutes and standard deviation 2.6 minutes. The restaurant manager wants to find the probability that the mean wait time will be greater than 12.0 minutes for a random sample of 84 customers. Assuming the wait times among customers are independent, which of the following describes the sampling distribution of the sample mean wait time for random samples of size 84 ?

Approximately normal with mean 11.4 minutes and standard deviation 2.6/√84 minute. B

Animal researchers studying cows and horses conducted a two-sample t-test for a difference in means to investigate whether grazing cows eat more grass, on average, than grazing horses. All conditions for inference were met, and the test produced a test statistic of t = 1.664 and a p-value of 0.0487. Which of the following is a correct interpretation of the p-value?

Assuming that the mean amount of grass eaten by cows is equal to the mean amount of grass eaten by horses, the probability of observing a test statistic of at least 1.664 is 0.0487

Researchers on car safety studied driver reaction time and cell phone use while driving. Participants in the study talked on either a hands-free phone or a handheld phone while driving in a car simulator. A two-sample t-test for a difference in means was conducted to investigate whether the mean driver reaction time between the two groups of participants was different. All conditions for inference were met, and the test produced a test statistic of t = -2.763 and a p-value of 0.03. Which of the following is a correct interpretation of the p-value?

Assuming that the mean reaction times for hands-free and handheld phones are equal, the probability of obtaining a test statistic greater than 2.763 or less than -2.763 is 0.03.

To determine whether employees at Site X have higher salaries, on average, than employees at Site Y of the same company do, independent random samples of salaries were obtained for the two groups. The data are summarized below. Based on the data, which of the following statements is true?

At the 5% significance level, employees at Site X have a significantly higher mean salary than employees at Site Y do.

According to government data, 22 percent of children in the United States under the age of 6 years live in households with incomes that are classified at a particular income level. A simple random sample of 300 children in the United States under the age of 6 years was selected for a study of learning in early childhood. If the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (Note: z represents a standard normal random variable.)

B

For a certain population of sea turtles, 18 percent are longer than 6.5 feet. A random sample of 90 sea turtles will be selected. What is the standard deviation of the sampling distribution of the sample proportion of sea turtles longer than 6.5 feet for samples of size 90 ?

B −√0.18(1-0.18)/90

A polling firm is interested in surveying a representative sample of registered voters in the United States. The firm has automated its sampling so that random phone numbers within the United States are called. Each time a number is called, the procedure below is followed. • If there is no response or if an answering machine is reached, another number is automatically called. • If a person answers, a survey worker verifies that the person is at least 18 years of age. • If the person is not at least 18 years of age, no response is recorded, and another number is called. • If the person is at least 18 years of age, that person is surveyed. Some people claim the procedure being used does not permit the results to be extended to all registered voters. Which of the following is NOT a legitimate concern about the procedure being used?

Registered voters with unlisted telephone numbers may be underrepresented in the sample.

At a large corporation, 6,000 employees from department A and 4,000 employees from department B are attending a training session. A random sample of 500 employees attending the session will be selected. Consider two sampling methods: with replacement and without replacement. How will the methods affect the standard deviations of the sampling distribution of the sample proportion of employees from department B?

Sampling without replacement will result in a standard deviation less than but close to \sqrt{\frac{0.4\left(0.6\right)}{500}}.5000.4(0.6)​​.

A city has designed a survey to collect information about residents' opinions about city services. Which of the following describes a scenario in which nonresponse bias is likely present?

Surveys were mailed to 500 people, and 200 of the surveys were completed and returned.

An experiment will be conducted in which 20 pepper plants are randomly assigned to two groups. The plants in Group 1 will receive the current fertilizer, Fertilizer A, and the plants in Group 2 will receive a new fertilizer, Fertilizer B. All other growing conditions, including amount of sunlight and water, will be kept the same for the two groups. The growth of the pepper plants will be compared for the two groups. What are the experimental units in this experiment?

The 20 plants in the two groups

In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

City officials estimate that 46 percent of all city residents are in favor of building a new city park. A random sample of 150 city residents will be selected. Suppose that 51 percent of the sample are in favor of building a new city park. Which of the following is true about the sampling distribution of the sample proportion for samples of size 150 ?

The distribution is approximately normal, and the mean is 0.46.

The histogram above shows the number of minutes needed by 45 students to finish playing a computer game. Which of the following statements is correct?

The distribution is skewed to the left.

Data will be collected on the following variables. Which variable is most likely to be approximated by a normal model?

The distribution of life span, in minutes, for batteries of a certain size, where most life spans cluster around the center of the distribution but with some very low and some very high life spans

A manufacturer of cell phone batteries claims that the average number of recharge cycles for its batteries is 400. A consumer group will obtain a random sample of 100 of the manufacturer's batteries and will calculate the mean number of recharge cycles. Which of the following statements is justified by the central limit theorem?

The distribution of the sample means of the number of recharge cycles is approximately normal because the sample size of 100 is greater than 30.

A manufacturer of cell phone batteries claims that the average number of recharge cycles for its batteries is 400. A consumer group will obtain a random sample of 100 of the manufacturer's batteries and will calculate the mean number of recharge cycles. Which of the following statements is justified by the central limit theorem?

The distribution of the sample means of the number of recharge cycles is approximately normal because the sample size of 100 is greater than 30. D

An experiment will be conducted to test the effectiveness of a weight-loss supplement. Volunteers will be randomly assigned to take either the supplement or a placebo for 90 days, with 12 volunteers in each group. The subjects will not know which treatment they receive. At the end of the experiment, researchers plan to calculate the mean weight loss for each of the two groups and to construct a two-sample t-confidence interval for the difference of the two treatment means. Which of the following assumptions is necessary for the confidence interval to be valid?

The distributions of weight loss of the two treatments are approximately normally distributed.

Based on records kept at a gas station, the distribution of gallons of gas purchased by customers is skewed to the right with mean 10 gallons and standard deviation 4 gallons. A random sample of 64 customer receipts was selected, and the sample mean number of gallons was recorded. Suppose the process of selecting a random sample of 64 receipts and recording the sample mean number of gallons was repeated for a total of 100 samples. Which of the following is the best description of a dotplot created from the 100 sample means?

The dotplot is approximately normal with mean 10 gallons and standard deviation 0.5 gallon. D

A certain statistic will be used as an unbiased estimator of a parameter. Let J represent the sampling distribution of the estimator for samples of size 40, and let K represent the sampling distribution of the estimator for samples of size 100. Which of the following must be true about J and K ?

The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

One statistic calculated for pitchers in baseball is called the earned run average, or ERAERA. The following boxplots summarize the ERAERA for pitchers in two leagues, A and B. Based on the boxplots, which of the following statistics is the same for both leagues?

The interquartile range

A city planner is investigating traffic congestion at a certain intersection. To collect data, a camera will record the number of cars that pass through the intersection at different hours of the day and on different days of the week. Which of the following best describes the type of investigation being conducted by the city planner?

The investigation is an observational study because treatments are not imposed.

Data were collected on the number of days per week that members visit a certain fitness center. The values varied from 0 to 7, and a distribution of relative frequencies for the values was created. Let the random variable X represent the number of days per week that a member visits. The mean of X is 3.12. Which of the following statements is the best interpretation of the mean?

The long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.

In 2014, 85 percent of households in the United States had a computer. For a randomly selected sample of 200 households in 2014, let the random variable C represent the number of households in the sample that had a computer. What are the mean and standard deviation of C?

The mean is 170 households, and the standard deviation is 5.05 households.

The following histogram shows the ages, in years, of the people who attended a documentary at a movie theater. Based on the histogram, which of the following statements best describes the relationship between the mean and the median of the distribution of ages?

The mean is most likely less than the median because the distribution is skewed to the left.

A national charity contacted 100 randomly selected people by phone, and 7 percent of those contacted made a donation to the charity. The population proportion of those who make a donation when contacted by phone is known to be p = 0.05. For samples of size 100, which of the following best interprets the mean of the sampling distribution of the sample proportion of people who make a donation when contacted by phone?

The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.

A national charity contacted 100 randomly selected people by phone, and 7 percent of those contacted made a donation to the charity. The population proportion of those who make a donation when contacted by phone is known to be p=0.05p=0.05. For samples of size 100, which of the following best interprets the mean of the sampling distribution of the sample proportion of people who make a donation when contacted by phone?

The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.

One way to measure the duration of subterranean disturbances such as earthquakes and mining is to calculate the root-mean-square time. The following histograms summarize the distributions of the root-mean-square times for two sources of disturbances. Based on the histograms, which of the following correctly compares the two distributions?

The median of the earthquake disturbances is less than the median of the mining disturbances.

A statistics student wants to compare the mean times needed to access flight information for two major airlines. Twenty randomly selected students accessed one airline's Web site, and the time required to locate the flight information using the Web site had a mean of 2.5 minutes and a standard deviation of 0.8 minute. Twenty different randomly selected students accessed the other airline's Web site, and the time required to locate the flight information using the Web site had a mean of 2.1 minutes and a standard deviation of 1.1 minutes. Assuming that the conditions for inference are met, which of the following statements about the p-value obtained from the data and the conclusion of the significance test is true?

The p-value is greater than 0.10; therefore, there is no significant difference in mean search times on the two Web sites.

A restaurant manager collected data on the number of customers in a party in the restaurant and the time elapsed until the party left the restaurant. The manager computed a correlation of 0.78 between the two variables. What information does the correlation provide about the relationship between the number of customers in a party at the restaurant and the time elapsed until the party left the restaurant?

The parties with a larger number of customers are associated with the LONGER times elapsed until the party left the restaurant.

The distribution of ocean wave height at a certain California beach is approximately normal with mean 7.2 feet. The distribution of ocean wave height at a certain Florida beach is approximately normal with mean 6.6 feet. Six waves from each beach will be selected at random and the heights will be recorded. Let x¯Cx¯C represent the sample mean height of the 6 California waves, and let x¯Fx¯F represent the sample mean height of the 6 Florida waves. Which of the following is the best interpretation of P(x¯C−x¯F>0.5)=0.55P(x¯C−x¯F>0.5)=0.55 ?

The probability of observing a difference (California minus Florida) greater than 0.5 feet between the mean height of 6 California waves and the mean height of 6 Florida waves is 0.55.

The distribution of ocean wave height at a certain California beach is approximately normal with mean 7.2 feet. The distribution of ocean wave height at a certain Florida beach is approximately normal with mean 6.6 feet. Six waves from each beach will be selected at random and the heights will be recorded. Let x‾CxC​ represent the sample mean height of the 6 California waves, and let x‾FxF​represent the sample mean height of the 6 Florida waves. Which of the following is the best interpretation of P(x‾C−x‾F>0.5)=0.55?P(xC​−xF​>0.5)=0.55?

The probability of observing a difference (California minus Florida) greater than 0.5 feet between the mean height of 6 California waves and the mean height of 6 Florida waves is 0.55.

A researcher conducted an experiment to study the effects of an herbal supplement on the duration of the common cold. From a sample of 50 people who had a cold, the researcher assigned 25 people to take the supplement each day. The other 25 people were asked to drink water each day and were not given the supplement. The researcher recorded the number of days the cold lasted for each person. What are the experimental units of the study?

The sample of 50 people who had a cold

At a large university, the division of computing services surveyed a random sample of 45 biology majors and 55 business majors from populations of over 1,000 biology and 1,000 business majors. The sampled students were asked how many hours they spend per week using any university computer lab. Let x¯1x¯1 represent the average hours per week spent in any university computer lab by the 45 biology majors, and let x¯2x¯2 represent the average hours per week spent in any university computer lab by the 55 business majors. Which of the following is the best explanation for why the sampling distribution of x¯1−x¯2x¯1−x¯2 can be modeled with a normal distribution?

The sample sizes are both sufficiently large.

At a large university, the division of computing services surveyed a random sample of 45 biology majors and 55 business majors from populations of over 1,000 biology and 1,000 business majors. The sampled students were asked how many hours they spend per week using any university computer lab. Let x‾1x1​ represent the average hours per week spent in any university computer lab by the 45 biology majors, and let x‾2x2​ represent the average hours per week spent in any university computer lab by the 55 business majors. Which of the following is the best explanation for why the sampling distribution of x‾1−x‾2x1​−x2​ can be modeled with a normal distribution?

The sample sizes are both sufficiently large.

A certain county school district has 15 high schools. The high school seniors' plans after graduation in each school vary greatly from one school to the next. The county superintendent will select a sample of high school seniors from the district to survey about their plans after graduation. The superintendent will use a cluster sample with the high schools as clusters. A random sample of 5 high schools will be selected, and all seniors at those high schools will complete the survey. What is one disadvantage to selecting a cluster sample to investigate the superintendent's goal?

The schools in the cluster sample might not be representative of the population of seniors.

Eighteen individuals who use a particular form of social media were assigned a new user interface to use when logging in to their accounts. After using the new user interface for a week, each individual was asked to rate how easy or hard the new user interface was to use on a scale from 1 (extremely easy) to 9 (extremely hard). Which of the following correctly identifies why this is not a well-designed experiment?

The study was not comparative—only one treatment was used.

Data were collected on 100 United States coins minted in 2018. Which of the following represents a quantitative variable for the data collected?

The value of the coin

The director of a marketing department wants to estimate the proportion of people who purchase a certain product online. The director originally planned to obtain a random sample of 2,500 people who purchased the product. However, because of budget concerns, the sample size will be reduced to 1,500 people. Which of the following describes the effect of reducing the number of people in the sample?

The variance of the sampling distribution of the estimator will increase. C

Two 99 percent confidence intervals will be constructed to estimate the difference in means of two populations, R and W. One confidence interval, I9,I9​, will be constructed using samples of size 9 from each of R and W, and the other confidence interval, I81,I81​, will be constructed using samples of size 81 from each of R and W. When all other things remain the same, which of the following describes the relationship between the two confidence intervals?

The width of I81I81​ will be 1331​ the width of I9.I9​.

A survey of 57 students was conducted to determine whether or not they held jobs outside of school. The two-way table above shows the number of students by employment status (job, no job), and class (juniors, seniors). Which of the following best describes the relationship between employment status and class?

There appears to be an association, since the proportion of juniors having jobs is much larger than the proportion of seniors having jobs.

A two-sample t-test for a difference in means was conducted to investigate whether the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke. With all conditions for inference met, the test produced a test statistic of t = -2.073 and a p-value of 0.042. Based on the p-value and a significance level of α=0.05,α=0.05, which of the following is a correct conclusion?

There is convincing statistical evidence that the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke.

A tennis ball was thrown in the air. The height of the ball from the ground was recorded every millisecond from the time the ball was thrown until it reached the height from which it was thrown. The correlation between the time and height was computed to be 0. What does this correlation suggest about the relationship between the time and height?

There is no linear relationship between time and height.

Each person in a simple random sample of 2,000 received a survey, and 317 people returned their survey. How could nonresponse cause the results of the survey to be biased?

Those who did respond may differ in some important way from those who did not respond.

The following table shows data for the 8 longest roller coasters in the world as of 2015. Which of the following variables is categorical?

Type

A recent study was conducted in which a random sample of men and a random sample of women were surveyed about whether they were fans of a professional football team. The study found that 39 percent of men in the sample were fans and 22 percent of women in the sample were fans. A 99 percent confidence interval for the difference in the proportion of fans of a professional football team between men and women was reported as (0.133, 0.207) Which of the following statements is the best interpretation of the interval?

We are 99% confident that the difference in the population percents of men and women who are fans of a professional football team is between 13.3% and 20.7%

A two-sample t-test for a difference in means will be conducted to investigate mean gasoline prices in two states. From each state, 45 gasoline stations will be selected at random. On the same day, the price of regular gasoline will be recorded for each selected station and the sample mean price for each state will be calculated. Have all conditions for inference been met?

Yes, all conditions have been met.

Researchers investigated whether there is a difference between two headache medications, R and S. Researchers measured the mean times required to obtain relief from a headache for patients taking one of the medications. From a random sample of 75 people with chronic headaches, 38 were randomly assigned to medication R and the remaining 37 were assigned to medication S. The time, in minutes, until each person experienced relief from a headache was recorded. The sample mean times were calculated for each medication. Have the conditions been met for inference with a confidence interval for the difference in population means?

Yes, all conditions have been met.

Random samples of players for two types of video games were selected, and the mean number of hours per week spent playing the games was calculated for each group. The sample means were used to construct the 90 percent confidence interval ( 1.5, 3.8 ) for the difference in the mean number of hours per week spent playing the games. The maker of one of the video games claims that there is a difference in the population mean number of hours per week spent playing the two games. Is the claim supported by the interval?

Yes, because 0 is not contained in the interval.

The mean and standard deviation of the sample data collected on continuous variable x are -0.25 and 0.03, respectively. The following table shows the relative frequencies of the data in the given intervals. IntervalRelative Frequency-0.34\le x\le-0.31−0.34≤x≤−0.310.02-0.31\le x\le-0.28−0.31≤x≤−0.280.15-0.28\le x\le-0.25−0.28≤x≤−0.250.33-0.25\le x\le-0.22−0.25≤x≤−0.220.36-0.22\le x\le-0.19−0.22≤x≤−0.190.11-0.19\le x\le-0.16−0.19≤x≤−0.160.03 Based on the table, do the data support the use of a normal model to approximate population characteristics?

Yes, because the distribution of relative frequencies is very close to the empirical rule for normal models.

The mean and standard deviation of the sample data collected on continuous variable x are -0.25 and 0.03, respectively. The following table shows the relative frequencies of the data in the given intervals. IntervalRelative Frequency−0.34≤x≤−0.31−0.34≤x≤−0.310.02−0.31≤x≤−0.28−0.31≤x≤−0.280.15−0.28≤x≤−0.25−0.28≤x≤−0.250.33−0.25≤x≤−0.22−0.25≤x≤−0.220.36−0.22≤x≤−0.19−0.22≤x≤−0.190.11−0.19≤x≤−0.16−0.19≤x≤−0.160.03 Based on the table, do the data support the use of a normal model to approximate population characteristics?

Yes, because the distribution of relative frequencies is very close to the empirical rule for normal models.

Researchers are studying two populations of wild horses living in the western regions of a country. In a random sample of 32 horses taken from the first population, the mean age of the sample was 21 years. In a random sample of 41 horses from the second population, the mean age of the sample was 19 years. Is the sampling distribution of the difference in sample mean ages approximately normal?

Yes, because the sample sizes are both greater than 30.

A state educational agency was concerned that the salaries of public school teachers in one region of the state,region A, were higher than the salaries in another region of the state, region B. The agency took two independent random samples of salaries of public school teachers, one from region A and one from region B. The data are summarized in the table below. Assuming all conditions for inference are met, do the data provide convincing statistical evidence that the salaries of public school teachers in region A are, on average, greater than the salaries of public school teachers in region B?

Yes, there is evidence at the significance level of α = 0.05 but not at α = 0.01.

At a large corporation, the distribution of years of employment for the employees has mean 20.6 years and standard deviation 5.3 years. A random sample of 100 employees was selected and surveyed about employee satisfaction. The sample of employees had a mean 20.3 years and standard deviation 6.1 years. Remy claims that the mean of the sampling distribution of the sample mean for samples of size 100 is 20.6 years. Is Remy's claim correct?

Yes. The mean of the sampling distribution is 20.6 years.

At a large corporation, the distribution of years of employment for the employees has mean 20.6 years and standard deviation 5.3 years. A random sample of 100 employees was selected and surveyed about employee satisfaction. The sample of employees had a mean 20.3 years and standard deviation 6.1 years. Remy claims that the mean of the sampling distribution of the sample mean for samples of size 100 is 20.6 years. Is Remy's claim correct?

Yes. The mean of the sampling distribution is 20.6 years. E

A company that makes fleece clothing uses fleece produced from two farms, Northern Farm and Western Farm. Let the random variable X represent the weight of fleece produced by a sheep from Northern Farm. The distribution of X has mean 14.1 pounds and standard deviation 1.3 pounds. Let the random variable Y represent the weight of fleece produced by a sheep from Western Farm. The distribution of Y has mean 6.7 pounds and standard deviation 0.5 pound. Assume X and Y are independent. Let W equal the total weight of fleece from 10 randomly selected sheep from Northern Farm and 15 randomly selected sheep from Western Farm. Which of the following is the standard deviation, in pounds, of W ?

\sqrt{10\left(1.3\right)^2+15\left(0.5\right)^2}10(1.3)2+15(0.5)2​

For a certain population of sea turtles, 18 percent are longer than 6.5 feet. A random sample of 90 sea turtles will be selected. What is the standard deviation of the sampling distribution of the sample proportion of sea turtles longer than 6.5 feet for samples of size 90 ?

\sqrt{\frac{0.18\left(1-0.18\right)}{90}}900.18(1−0.18)​​

At a manufacturing company for medical supplies, machines produce parts used in highly specialized lasers. Company researchers are testing a new machine designed to improve the precision of the parts. The null hypothesis is that the new machine does not improve the precision. For the researchers, the more consequential error would be that the new machine actually improves the precision, but the test does not detect the improvement. Which of the following should the researchers do to avoid the more consequential error? A Increase the significance level to increase the probability of a Type I error. B Increase the significance level to decrease the probability of a Type I error. C Decrease the significance level to increase the probability of a Type I error. D Decrease the significance level to decrease the probability of a Type I error. E Decrease the significance level to decrease the standard error.

a

A fair six-sided die, with sides numbered 1 through 6, will be rolled a total of 15 times. Let x¯1 represent the average of the first ten rolls, and let x¯2represent the average of the remaining five rolls. What is the mean μ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2 ?

b. 3.5−3.5=0

At a large university, the division of computing services surveyed a random sample of 45 biology majors and 55 business majors from populations of over 1,000 biology and 1,000 business majors. The sampled students were asked how many hours they spend per week using any university computer lab. Let x¯1 represent the average hours per week spent in any university computer lab by the 45 biology majors, and let x¯2 represent the average hours per week spent in any university computer lab by the 55 business majors.

b. The sample sizes are both sufficiently large.

Approximately 52 percent of all recent births were boys. In a simple random sample of 100 recent births, 49 were boys and 51 were girls. The most likely explanation for the difference between the observed results and the expected results in this case is

b. variability due to sampling

A random sample of 300 students is selected from a large group of students who use a computer-equipped classroom on a regular basis. Occasionally, students leave their USB drive in a computer. Of the 300 students questioned, 180 said that they write their name on their USB drive. Which of the following is a 98 percent confidence interval for the proportion of all students using the classroom who write their name on their USB drive? A 0.4±2.33(0.4)(0.6)300−−−−−−√ B 0.4±1.96(0.4)(0.6)300−−−−−−√ C 0.6±2.33(0.6)(0.4)300−−−−−−√ D 0.6±1.96(0.6)(0.4)300−−−−−−√ E 0.6±2.05(0.6)(0.4)300−−−−−−√

c

A random sample of residents in city J were surveyed about whether they supported raising taxes to increase bus service for the city. From the results, a 95 percent confidence interval was constructed to estimate the proportion of people in the city who support the increase. The interval was (0.46,0.52). Based on the confidence interval, which of the following claims is supported? A More than 90 percent of the residents support the increase. B More than 60 percent of the residents support the increase. C More than 40 percent of the residents support the increase. D Fewer than 10 percent of the residents support the increase. E Fewer than 25 percent of the residents support the increase.

c

The germination rate is the rate at which plants begin to grow after the seed is planted. A seed company claims that the germination rate for their seeds is 90 percent. Concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. What are the correct hypotheses for a one-sample z-test for a population proportion p ? A H0:p=0.80Ha:p<0.80 B H0:p=0.80Ha:p>0.80 C H0:p=0.90Ha:p<0.90 D H0:p=0.90Ha:p>0.90 E H0:p=0.90Ha:p≠0.90

c

The management team of a company with 10,000 employees is considering installing charging stations for electric cars in the company parking lots. In a random sample of 500 employees, 15 reported owning an electric car. Which of the following is a 99 percent confidence interval for the proportion of all employees at the company who own an electric car? A B C D E

c

To investigate whether there is a difference in opinion on a certain proposal between two voting districts, A and B, two independent random samples were taken. From district A, 35 of the 50 voters selected were in favor of the proposal, and from district B, 36 of the 60 voters selected were in favor of the proposal. Which of the following is the test statistic for the appropriate test to investigate whether there is a difference in the proportion of voters who are in favor of the proposal between the two districts (district A minus district B)? A 35−363550+3660√ B 35−360.750+0.660√ C 0.7−0.6(0.65)(0.35)(150+160)√ D 0.7−0.6(0.7)(0.6)(150+60)√ E 0.7−0.6(0.7)(0.6)150+160√

c

Which of the following gives the probability of making a Type I error? A The sample size B The power C The significance level D The standard error E The p-value

c

Suppose the variance in trunk diameter of the giant sequoia tree species is 15.7m2, while the variance in trunk diameter of the California redwood tree species is 10.6m2. Let x¯1 represent the average trunk diameter of four randomly sampled giant sequoia trees, and let x¯2represent the average trunk diameter of three randomly sampled California redwood trees. If the random sampling is done with replacement, what is the standard deviation σ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2 ?

c.

A certain skin cream is 80 percent effective in curing a common rash. A random sample of 100 people with the rash will use the cream. Which of the following is the best description of the shape of the sampling distribution of the sample proportion of those who will be cured?

c. Approximately normal

Two different drugs, X and Y, are currently in use to treat a certain condition. About 7 percent of the people using either drug experience side effects. A random sample of 75 people using drug X and a random sample of 150 people using drug Y are selected. The proportion of people in each sample who experience side effects is recorded.

c. No. The sample size for drug Y is large enough, but the sample size for drug X is not.

The manager of a magazine wants to estimate the percent of magazine subscribers who approve of a new cover format. To gather data, the manager will select a random sample of subscribers. Which of the following is the most appropriate interval for the manager to use for such an estimate? A A two-sample z-interval for a difference between sample proportions B A two-sample z-interval for a difference between population proportions C A one-sample z-interval for a sample proportion D A one-sample z-interval for a population proportion E A one-sample z-interval for a difference between population proportions

d

City R is a large city with 4 million residents, and City S is a smaller city with 0.25 million residents. Researchers believe that the proportion of City S residents who regularly ride bicycles is between 10 percent and 25 percent and the proportion of City R residents who regularly ride bicycles is between 20 percent and 50 percent.

d. 50 in City R and 100 in City S

A representative of a car manufacturer in the United States made the following claim in a news report. Ten years ago, only 53 percent of Americans owned American-made cars, but that figure is significantly higher today. A research group conducted a study to investigate whether the claim was true. The group found that 56 percent of a randomly selected sample of car owners in the United States owned American-made cars. A test of the appropriate hypotheses resulted in a p-value of 0.283. Assuming the conditions for inference were met, is there sufficient evidence to conclude, at the significance level of a = 0.05, that the proportion of all car owners in the United States who own American-made cars has increased from what it was ten years ago? A Yes, because 0.56 > 0.53. B Yes, because a reasonable interval for the proportion is 0.56 ± 0.283. C Yes, because 0.56 - 0.53 = 0.03 and 0.03 < 0.05. D No, because 0.283 < 0.53. E No, because 0.283 > 0.05.

e

In order to make statistical inferences when testing a population proportion p, which of the following conditions verify that inference procedures are appropriate? The data are collected using a random sample or random assignment. The sample size is less than 10 percent of the population size. np0≥10 and n(1−p0)≥10 for sample size n and hypothesized proportion p0. A I only B II only C III only D II and III only E I, II, and III

e

Jessica wanted to determine if the proportion of males for a certain species of laboratory animal is less than 0.5. She was given access to appropriate records that contained information on 12,000 live births for the species. To construct a 95 percent confidence interval, she selected a simple random sample of 100 births from the records and found that 31 births were male. Based on the study, which of the following expressions is an approximate 95 percent confidence interval estimate for p, the proportion of males in the 12,000 live births? A B C D E

e

Two non-profit organizations, L and M, accept donations from people. In a certain month, 140 people donated to organization L, with an average donation amount of x¯L=$113, and 42 people donated to organization M, with an average donation amount of x¯M=$390.

e. Dollars

Samples G and H were selected from the same population of quantitative data and the mean of each sample was determined. The mean of sample G is equal to the mean of the population.

e. II and III

A certain statistic will be used as an unbiased estimator of a parameter. Let J represent the sampling distribution of the estimator for samples of size 40, and let K represent the sampling distribution of the estimator for samples of size 100.

e. The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.

A recent report indicated that 90 percent of adults in a certain region actively try to include vegetables in their diet. A simulation was conducted that consisted of 50 trials with a population parameter of 0.9. Each trial consisted of a sample size of 10. The number of successes out of 10 was recorded, where success represented an adult trying to include vegetables in the diet. Five possible simulation results are shown. Which simulation is the best match to the one described?

highest at nine, really tall

Which of the following pairs of sample size n and population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion p̂?

n = 100 and p close to 1/2. E

The probability of winning a certain game is 0.5. If at least 70 percent of the games in a series of n games are won, the player wins a prize. If the possible choices for n are n=10, n=20, and n=100, which value of n should the player choose in order to maximize the probability of winning a prize?

n=10 only

A recent survey concluded that the proportion of American teenagers who have a cell phone is 0.27. The true population proportion of American teenagers who have a cell phone is 0.29. For samples of size 1,000 that are selected at random from this population, what are the mean and standard deviation, respectively, for the sampling distribution of the sample proportion of American teenagers who have a cell phone?

o.29, sqr (0.29)(0.71)/1000

The histogram below represents data obtained after the census of an entire population was conducted. The sampling distribution of the sample mean based on samples of size 2 for the population was simulated, and a histogram of the results was produced. Which of the following histograms is most likely the histogram of that sampling distribution?

one big in middle and small bumps on edges

In two common species of flowers, A and B, the proportions of flowers that are blue are papa and pbpb , respectively. Suppose that independent random samples of 50 species-A flowers and 100 species-B flowers are selected. Let pˆap^a be the sample proportion of blue species-A flowers and pˆbp^b be the sample proportion of blue species-B flowers. What is the mean of the sampling distribution of pˆa−pˆbp^a−p^b ?

pa−pb

Carla wants to investigate whether a person's political party affiliation causes the person to be more vocal about political issues. She plans to administer a survey to a large sample of people. Which of the following describes why the method of data collection used will prevent Carla from achieving her goal?

Causation cannot be determined from a survey.

An observational study found that the amount of sleep an employee gets each night is associated with job performance. The correlation coefficient was found to be r=0.86r=0.86. A reader of the study concluded that more sleep causes employees to perform better. Why is such a conclusion not correct?

Causation cannot be determined from an observational study.

A researcher calculated sample proportions from two independent random samples. Assuming all conditions for inference are met, which of the following is the best method for the researcher to use to estimate the true difference between the population proportions?

Construct a two-sample z-interval for the difference between population proportions.

A local arts council has 200 members. The council president wanted to estimate the percent of its members who have had experience in writing grants. The president randomly selected 30 members and surveyed the selected members on their grant-writing experience. Of the 30 selected members, 12 indicated that they did have the experience. Have the conditions for inference with a one-sample z-interval been met? A Yes, all conditions for inference have been met. B No, because the sample size is not large enough to satisfy the conditions for normality. C No, because the sample was not selected at random. D No, because the sample size is not less than 10 percent of the population size. E No, because the sample is not representative of the population.

D

A sociologist will conduct a two-sample t-test for a difference in means to investigate whether there is a significant difference, on average, between the salaries of people with bachelor's degrees and people with master's degrees. From a random sample of 32 people with a bachelor's degree, the average salary was $55,000 with standard deviation $3,500. From a random sample of 28 people with a master's degree, the average salary was $58,000 with a standard deviation of $4,000. With a null hypothesis of no difference in the means, which of the following is the test statistic for the appropriate test to investigate whether there is a difference in population means (master's degree minus bachelor's degree) ?

t=284,0002​+323,5002​​(58,000−55,000)​

A two-sample t-test for a difference in means will be conducted to investigate whether the average length of a cell phone call is shorter this year compared with 5 years ago. From a random sample of 35 phone call records this year, the average length was 25 minutes with a standard deviation of 4 minutes. From a random sample of 32 phone call records from 5 years ago, the average length was 27 minutes with a standard deviation of 5 minutes. The difference (this year minus five years ago) in means will be calculated. With a null hypothesis of no difference in length, which of the following is a correct test statistic for the test?

t=3542​+3252​​25−27​

From a random sample of 185 children from school G, 108 indicated they wanted to study science in college. From a different random sample of 165 children from school H, 92 indicated they wanted to study science in college. Assuming all conditions for inference are met, which of the following is closest to the standard error for a confidence interval for the difference in population proportions between the two schools of children who want to study science in college?

two parentheses, over a divider, plus another of the same, square rooted

Consider n pairs of numbers (x1,y1), (x2,y2), ..., and (xn, yn). The mean and standard deviation of the x-values are x̄ =5 and sx = 4, respectively. The mean and standard deviation of the y-values are ȳ = 10 and sy = 10 respectively. Of the following, which could be the least squares regression line?

ŷ = 8.5 + 0.3x

The statistic x¯ is used as an estimator for which of the following?

μ

A company that ships crystal bowls claims that bowls arrive undamaged in 95 percent of the shipments. Let the random variable G represent the number of shipments with undamaged bowls in 25 randomly selected shipments. Random variable G follows a binomial distribution with a mean of 23.75 shipments and a standard deviation of approximately 1.09 shipments. Which of the following is the best interpretation of the mean?

For all possible shipments of size 25, the average number of undamaged shipments is equal to 23.75.

The manager of a symphony in a large city wants to investigate music preferences for adults and students in the city. Let p_ApA​ represent the population proportion of adults who live in the city who prefer pop music. Let p_SpS​ represent the population proportion of students who live in the city who prefer pop music. Random samples of 200 adults from the city and 200 students from the city will be selected.

For all random samples of 200 adults from the city and 200 students from the city, the sample proportion of adults who prefer pop music will be greater than the sample proportion of students who prefer pop music in about 2.2% of samples.

symphony one

For all random samples of 200 adults from the city and 200 students from the city, the sample proportion of adults who prefer pop music will be greater than the sample proportion of students who prefer pop music in about 2.2% of samples.

On any given day, the proportion of workers at a factory who are more than 5 minutes late to work is 0.11. A random sample of 20 workers will be selected. Which of the following is the best interpretation of the mean of the sampling distribution of the sample proportion of workers in the sample who are more than 5 minutes late to work for samples of size 20 ?

For all samples of size 20, the mean of all possible sample proportions is equal to 0.11.

A manufacturer of cell phone screens has found that 5 percent of all screens produced have defects. Let p_dpd​ represent the population proportion of all cell phone screens with a screen defect, therefore p_d=0.05pd​=0.05. For the sampling distribution of the sample proportion of cell phone screens from this manufacturer with a screen defect for sample size 400, \mu_{p_d}=0.05μpd​​=0.05. Which of the following is the best interpretation of \mu_{p_d}=0.05μpd​​=0.05?

For all samples of size 400 from this population, the mean of all resulting sample proportions of cell phone screens with a screen defect is 0.05.

At a certain high school, the distribution of backpack weight is approximately normal with mean 19.7 pounds and standard deviation 3.1 pounds. A random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded. For samples of size 5, which of the following is the best interpretation of P(x¯>22)≈0.05?

For all samples of size 5, the probability that the sample mean will be greater than 22 pounds is approximately 0.05.

At a certain high school, the distribution of backpack weight is approximately normal with mean 19.7 pounds and standard deviation 3.1 pounds. A random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded. For samples of size 5, which of the following is the best interpretation of P\left(\overline{x}>22\right)\approx0.05P(x>22)≈0.05?

For all samples of size 5, the probability that the sample mean will be greater than 22 pounds is approximately 0.05.

Exercise physiologists are investigating the relationship between lean body mass (in kilograms) and the resting metabolic rate (in calories per day) in sedentary males. Based on the computer output above, which of the following is the best interpretation of the value of the slope of the regression line?

For each additional kilogram of LEAN BODY MASS, the resting metabolic rate increases on average by 22.563 calories per day.

A sample of 100 students from Liberty High School and a sample of 60 students from Central High School were asked what they planned to do after graduation. Responses fell into five categories: four-year university (4Y)(4Y), community college (CC)(CC), join the workforce (W)(W), join the military (M)(M), or undecided (UD)(UD). The results are shown in the following bar chart. Which of the following statements is supported by the bar chart?

For the category undecided, the number of students from Liberty High School was 4 greater than the number of students from Central High School.

A penalty kick in soccer involves two players from different teams, the shooter and the goalie. During the penalty kick the shooter will try to score a goal by kicking a soccer ball to the left or right of the goal area. To prevent the shooter from scoring a goal, the goalie will move to the left or right of the goal area. The following table summarizes the directions taken by the shooter and the goalie for 372 penalty kicks. Which of the following indicates an association between the shooter's choice of direction and the goalie's choice of direction?

For the goalie, the relative frequency of a direction is not equal to the relative frequency conditioned on the shooter's direction

In a certain school district, students from grade 6 through grade 12 can participate in a school-sponsored community service activity. The following bar chart shows the relative frequencies of students from each grade who participate in the community service activity. Which of the following statements is supported by the bar chart?

Grade 12 had the least relative frequency of participating students.

poldactyl cats; toes; region A; region B

H0​:pa​−pb​=0 Ha:pa−pb>0Ha​:pa​−pb​>0

polydactyl cats region a region b

H0​:pa​−pb​=0 Ha:pa−pb>0Ha​:pa​−pb​>0

Two siblings, Alice and Sean, are both convinced that they are faster than the other at solving a puzzle cube. They recorded the length of time it took them to solve the cube 18 times each during a one-month period. Then each calculated the mean amount of time and standard deviation, in minutes, for their times. Let μAμA​ equal the mean time it took Alice to solve the puzzle cube and μSμS​equal the mean time it took Sean. Which of the following are the appropriate null and alternative hypotheses to test for a difference in time for the siblings to solve the cube?

Ho​:μA​−μS​=0 Ha:μA−μS≠0Ha​:μA​−μS​​=0

Two siblings, Alice and Sean, are both convinced that they are faster than the other at solving a puzzle cube. They recorded the length of time it took them to solve the cube 18 times each during a one-month period. Then each calculated the mean amount of time and standard deviation, in minutes, for their times. Let μAμA​ equal the mean time it took Alice to solve the puzzle cube and μSμS​equal the mean time it took Sean. Which of the following are the appropriate null and alternative hypotheses to test for a difference in time for the siblings to solve the cube?

Ho​:μA​−μS​=0 Ha:μA−μS≠0Ha​:μA​−μS​​=0 yes it's the one with the funny not equal sign

Cheryl practices hitting a softball in an indoor stadium by using both an aluminum bat and a composite bat made of carbon fiber and graphite. She records the distance traveled by the ball for each hit. Let x¯1x¯1 represent the average distance traveled by balls hit with the aluminum bat, and let x¯2x¯2 represent the average distance traveled by balls hit with the composite bat. Assume Cheryl's batting practice hits are independent. Which of the following conditions are sufficient to model the sampling distribution of x¯1−x¯2x¯1−x¯2 with a normal distribution? There are at least 30 recorded distances traveled for each type of bat. The distribution of distance traveled by the ball is approximately normal for each bat. The total number of distances traveled is at least 60 for the two bats combined.

I and II only

For which of the following is the shape of the sampling distribution of the sample mean approximately normal? A random sample of size 5 from a population that is approximately normal A random sample of size 10 from a population that is strongly skewed to the right A random sample of size 60 from a population that is strongly skewed to the left

I and III only

A two-sample t-test of the hypotheses H0 : μ1 - μ2 = 0 versus Ha : μ1- μ2 > 0 produces a p-value of 0.03. Which of the following must be true? I. A 90 percent confidence interval for the difference in means will contain the value 0. II. A 95 percent confidence interval for the difference in means will contain the value 0. III. A 99 percent confidence interval for the difference in means will contain the value 0.

II and III only

Researchers investigated whether a new process for producing yarn could reduce the mean amount of volatile organic compounds (VOCs) emitted by carpet. From random samples of carpets, the researchers found the mean reduction of VOCs emitted by carpets made with yarn produced by the new process compared with that of carpets made with yarn produced by the traditional process was 13 parts per million (ppm). All conditions for inference were met, and the p-value for the appropriate hypothesis test was 0.095. Which of the following statements is the best interpretation of the p-value?

If the null hypothesis is true, the probability of observing a mean reduction of at least 13 ppm is 0.095.

Biologists were studying the proportions of cats that had spotted markings on their fur in two populations of cats, C and F. An independent random sample of cats was taken from each population, and the difference between the sample proportions of cats with the spotted markings (C minus F) was 0.62. Under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being that the population proportions are not equal. The p-value of the test was 0.01. Which of the following is the correct interpretation of the p-value?

If the proportions of all cats with spotted markings is the same for both populations, the probability of observing a sample difference of at least 0.62 or at most -0.62 is 0.01.

In which of the following should the random variable X not be modeled with a geometric distribution?

In a bag of 30 different colored candies, about 20% are red. One candy will be selected one at a time without replacement, and its color will be recorded. Let X represent the number of candies selected before red is selected.

A local employer asked for help selecting a new type of desk chair. Thirty employees volunteered, and each employee used the new desk chair for two weeks and the current desk chair for two weeks. To determine which chair was used first, a coin was flipped for each employee. Heads represented using the new chair first, and tails represented using the current chair first. At the end of each two-week period, the employees were asked to rate their satisfaction with the new chair. Which of the following best describes this study?

It is a well-designed experiment because there is random assignment, replication, and comparison of at least two treatment groups.

Independent random samples of voters from two voting districts, G and H, were selected to investigate the proportion of all voters who favor a proposal to widen a road that runs through both districts. The difference between the sample proportions (G minus H) was used to create the 95 percent confidence interval (0.13, 0.47) for the population difference between districts. Which of the following is the best interpretation of the interval?

It is likely that more voters in district G favor the proposal than in district H, because all values in the interval are positive.

A researcher wanted to study the effects of a certain chemical on cell growth. The chemical was to be applied at two different doses, high and low, to two different cell types, strain A and strain B. Each combination of dose and cell type was to be replicated ten times. To have consistency from one replicate to the next, the researcher decided to use four lab technicians. One technician would be assigned the high dose with strain A. A second would be assigned the low dose with strain A. A third would be assigned the high dose with strain B. A fourth would be assigned the low dose with strain B. The assignment of lab technician to the replicates for a combination of dose and cell type would be randomized. A statistician told the researcher that the design could be improved by controlling confounding variables. Which of the following is potentially a confounding variable in this study?

Lab technician

A fair die has its faces numbered from 1 to 6. Let random variable FF represent the number landing face up when the die is tossed. The probability distribution for the random variable has mean 3.5 and standard deviation 1.7078. Consider a simulation with 400 trials designed to estimate the sampling distribution of the sample mean for 5 tosses of the die. For each trial, the die is tossed 5 times, and the mean of the 5 values landing face up is recorded. The mean and standard deviation of the results of the simulation should be close to which of the following?

Mean 3.5 and standard deviation 0.7638

A fair die has its faces numbered from 1 to 6. Let random variable F represent the number landing face up when the die is tossed. The probability distribution for the random variable has mean 3.5 and standard deviation 1.7078. Consider a simulation with 400 trials designed to estimate the sampling distribution of the sample mean for 5 tosses of the die. For each trial, the die is tossed 5 times, and the mean of the 5 values landing face up is recorded. The mean and standard deviation of the results of the simulation should be close to which of the following?

Mean 3.5 and standard deviation 0.7638. B

A reading specialist wanted to estimate the mean word length, in number of letters, for an elementary school history textbook. The specialist took repeated random samples of size 100 words and estimated the mean and standard deviation of the sampling distribution to be 4.9 letters and 0.15 letter, respectively. Based on the estimates for the sampling distribution, which of the following provides the best estimates of the population parameters?

Mean 4.9 letters and standard deviation 1.5 letters. C

A company wanted to determine the health care costs of its employees. A sample of 25 employees were interviewed and their medical expenses for the previous year were determined. Later the company discovered that the highest medical expense in the sample was mistakenly recorded as 10 times the actual amount. However, after correcting the error, the corrected amount was still greater than or equal to any other medical expense in the sample. Which of the following sample statistics must have remained the same after the correction was made?

Median

The following boxplot summarizes the heights of a sample of 100 trees growing on a tree farm. Emily claims that a tree height of 43 inches is an outlier for the distribution. Based on the 1.5×IQR1.5×IQR rule for outliers, is there evidence to support the claim?

NO, because 43 is NOT greater than (Q3+1.5×IQR)(Q3+1.5×IQR).

Two coins, A and B, each have a side for heads and a side for tails. When coin A is tossed, the probability it will land tails-side up is 0.5. When coin B is tossed, the probability it will land tails-side up is 0.8. Both coins will be tossed 20 times. Let pˆAp^A represent the proportion of times coin A lands tails-side up, and let pˆBp^B represent the proportion of times coin B lands tails-side up. Is the number of tosses for each coin enough for the sampling distribution of the difference in sample proportions pˆA−pˆBp^A−p^B to be approximately normal?

No, 20 tosses for coin A is enough, but 20 tosses for coin B is not enough.

For a specific species of fish in a pond, a wildlife biologist wants to build a regression equation to predict the weight of a fish based on its length. The biologist collects a random sample of this species of fish and finds that the lengths vary from 0.75 to 1.35 inches. The biologist uses the data from the sample to create a single linear regression model. Would it be appropriate to use this model to predict the weight of a fish of this species that is 3 inches long?

No, because 3 inches falls above the maximum value of lengths in the sample.

To check the effect of cold temperature on the elasticity of two brands of rubber bands, one box of Brand A and one box of Brand B rubber bands are tested. Ten bands from the Brand A box are placed in a freezer for two hours and ten bands from the Brand B box are kept at room temperature. The amount of stretch before breakage is measured on each rubber band, and the mean for the cold bands is compared to the mean for the others. Is this a good experimental design?

No, because temperature is confounded with brand.

A fitness center piloted two new programs to help people reduce stress levels and maintain a healthy lifestyle. After one month, 112 of the 125 people who volunteered for a program in mindfulness reported a reduction in stress levels, and 110 of the 135 people who volunteered for a yoga program reported a reduction in stress levels. The fitness center wants to investigate whether there is a significant difference between the proportions of all people in the two programs who would report reductions in stress levels. Have the conditions for inference been met?

No, because the samples were not selected or assigned using a random method.

For a population of leghorn chickens, the mean number of eggs laid per chicken is 0.70 with standard deviation 0.20 egg. For a population of Sussex chickens, the mean number of eggs laid per chicken is 0.50 with standard deviation 0.10 egg. Two independent random samples of chickens were taken from the populations. The following table shows the sample statistics. nx‾xsLeghorn360.750.30Sussex360.450.12 Mike claims that for all samples of size 36 from the population of leghorn chickens and all samples of size 36 from the population of Sussex chickens, the mean of all possible differences in sample means (leghorn minus Sussex) is 0.30 eggs per chicken. Is Mike's claim correct?

No. The mean is 0.70 - 0.50 = 0.20 egg per chicken.

A consumer group is investigating two brands of popcorn, R and S. The population proportion of kernels that will pop for Brand R is 0.90. The population proportion of kernels that will pop for Brand S is 0.85. Two independent random samples were taken from the population. The following table shows the sample statistics. The consumer group claims that for all samples of size 100 kernels from Brand R and 200 kernels from Brand S, the mean of all possible differences in sample proportions (Brand R minus Brand S) is 0.03. Is the consumer group's claim correct?

No. The mean is 0.90−0.85=0.050.90−0.85=0.05.

Two different drugs, X and Y, are currently in use to treat a certain condition. About 7 percent of the people using either drug experience side effects. A random sample of 75 people using drug X and a random sample of 150 people using drug Y are selected. The proportion of people in each sample who experience side effects is recorded. Are the sample sizes large enough to assume that the sampling distribution of the difference in sample proportions is approximately normal?

No. The sample size for drug Y is large enough, but the sample size for drug X is not.

The computer output below shows the result of a linear regression analysis for predicting the concentration of zinc, in parts per million (ppm), from the concentration of lead, in ppm, found in fish from a certain river. Which of the following statements is a correct interpretation of the value 19.0 in the output?

On average there is a predicted increase of 19.0 ppm in concentration of ZINC for every increase of 1 ppm in concentration of LEAD found in the fish.

The quality control manager at a factory records the number of equipment breakdowns each day. Let the random variable Y represent the number of breakdowns in one day. The standard deviation of Y is 0.28. Which of the following is the best interpretation of the standard deviation?

On average, the number of breakdowns per day varies from the mean by about 0.28.

Let the random variable Q represent the number of students who go to a certain teacher's office hour each day. The standard deviation of Q is 2.2. Which of the following is the best interpretation of the standard deviation?

On average, the number of students going to an office hour varies from the mean by about 2.2 students.

The continuous random variable N has a normal distribution with mean 7.5 and standard deviation 2.5. For which of the following is the probability equal to 0.156?

P(N = 8)

According to government data, 22 percent of children in the United States under the age of 6 years live in households with incomes that are classified at a particular income level. A simple random sample of 300 children in the United States under the age of 6 years was selected for a study of learning in early childhood. If the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (Note: z represents a standard normal random variable.)

P(z>300(0.22)(0.78)​​0.27−0.22​)

To estimate the percent of red marbles in a large bag of marbles, Margo will use the following sampling method. She will randomly select a marble, record its color, put it back into the bag, shake the bag to thoroughly mix the marbles, and then repeat those steps. She will perform the procedure many times. What type of sampling method is Margo using?

Random sampling with replacement

Researchers are investigating the effect of pHpH level in water on the breeding habits of the moon jellyfish. As part of a laboratory experiment, they will randomly assign one of three treatments, low pHpH, medium pHpH, or high pHpH, to the water in the tanks that hold the jellyfish. Which of the following is the best reason for the random assignment of a treatment level to an experimental unit?

Randomization tends to minimize the effects of uncontrolled variables, such as water temperature, so that such factors are not confounded with the treatment effects.

The following list shows the selling prices of 8 houses in a certain town. What is the median selling price of the houses in the list?

$283,300

The following scatterplot shows two variables, xx and yy, along with a least-squares model. Which of the following is a high leverage point with respect to the regression?

(80,70)

gardener seeds water germinate 95 percent confidence interval

I and III only

Data will be collected on the following variables. Which variable can be considered discrete?

The number of books a person finished reading last month

A certain factory that manufactures office chairs has a quality control process to identify defective chairs. The binomial random variable D represents the number of chairs in a sample of chairs that are defective. The mean of D is 10 chairs and the standard deviation is 3 chairs. Based on the distribution of D, which of the following would be an accurate interpretation of the value 0.1 ?

The probability of identifying a defective chair

At a college the scores on the chemistry final exam are approximately normally distributed, with a mean of 75 and a standard deviation of 12. The scores on the calculus final are also approximately normally distributed, with a mean of 80 and a standard deviation of 8. A student scored 81 on the chemistry final and 84 on the calculus final. Relative to the students in each respective class, in which subject did this student do better?

The student did equally well in each course.

A set of bivariate data was used to create a least-squares regression line. Which of the following is minimized by the line?

The sum of the squared residuals

The continuous random variable N has a normal distribution with mean 7.5 and standard deviation 2.5. For which of the following is the probability equal to 0 ?

a. P(N=8)

A city planner wants to estimate the proportion of city residents who commute to work by subway each day. A random sample of 30 city residents was selected, and 28 of those selected indicated that they rode the subway to work. Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal? A No, because the size of the population is not known. B No, because the sample is not large enough to satisfy the normality conditions. C Yes, because the sample is large enough to satisfy the normality conditions. D Yes, because the sample was selected at random. E Yes, because sampling distributions of proportions are modeled with a normal model.

b

A certain statistic dˆ is being used to estimate a population parameter D. The expected value of dˆ is not equal to D. What property does dˆexhibit?

e. dˆ is biased

95 percent confidence interval proportion difference supported by the interval

not sufficient evidence

The commuting time for a student to travel from home to a college campus is normally distributed with a mean of 30 minutes and a standard deviation of 5 minutes. If the student leaves home at 8:25 A.M., what is the probability that the student will arrive at the college campus later than 9 A.M.?

0.16

city health officials; fleas; cats; dogs

120-100 divided by the square root of 22 squared divided by 22 plus 30 squared over 15

A fair coin is flipped 10 times and the number of heads is counted. This procedure of 10 coin flips is repeated 100 times and the results are placed in a frequency table. Which of the frequency tables below is most likely to contain the results from these 100 trials?

22, 24, 18

A machine is used to fill bags with a popular brand of trail mix. The machine is calibrated so the distribution of the weights of the bags of trail mix is normal, with mean 240 grams and standard deviation 3 grams. Of the following, which is the least weight of a bag in the top 5 percent of the distribution?

234 grams

The histogram below displays the frequencies of waiting times, in minutes, for 175 patients in a dentist's office. Which of the following could be the median of the waiting times, in minutes?

7.25

According to 2015 census data, 42.7 percent of Colorado residents were born in Colorado. If a sample of 250 Colorado residents is selected at random, what is the standard deviation of the number of residents in the sample who were born in Colorado?

7.82

In a certain game, a fair die is rolled and a player gains 20 points if the die shows a "6." If the die does not show a "6," the player loses 3 points. If the die were to be rolled 100 times, what would be the expected total gain or loss for the player?

A gain of about 83 points

seeds; water; proportion of seeds

I and III only

A 99 percent confidence interval for a difference in means was given as 25.1±4.3.25.1±4.3. Assuming all conditions for inference were met, which of the following is a correct interpretation of the 99 percent confidence level?

In repeated samples of the same size, approximately 99 percent of the intervals constructed from the samples will capture the difference in population means.

Let S represent the number of randomly selected adults in a community surveyed to find someone with a certain genetic trait. The random variable S follows a geometric distribution with mean 4.66. Which of the following is a correct interpretation of the mean?

In repeated sampling from the distribution of S, the average of the values will approach 4.66.

A fair die has its faces numbered from 1 to 6. Let random variable F represent the number landing face up when the die is tossed. The probability distribution for the random variable has mean 3.5 and standard deviation 1.7078. Consider a simulation with 400 trials designed to estimate the sampling distribution of the sample mean for 5 tosses of the die. For each trial, the die is tossed 5 times, and the mean of the 5 values landing face up is recorded.

Mean 3.5 and standard deviation 0.7638

A reading specialist wanted to estimate the mean word length, in number of letters, for an elementary school history textbook. The specialist took repeated random samples of size 100 words and estimated the mean and standard deviation of the sampling distribution to be 4.9 letters and 0.15 letter, respectively. Based on the estimates for the sampling distribution, which of the following provides the best estimates of the population parameters?

Mean 4.9 letters and standard deviation 1.5 letters

Let random variable U represent the field goal percentage (percentage of shots made) for players in a basketball league. The following table shows the probability distribution of the random variable U. Field Goal PercentageProbability0.30.100.40.450.50.300.60.100.70.05 Fatima claims that the distribution of U is uniform with a median of 0.4 field goal percentage. Is Fatima's claim supported by the table?

No, the distribution is skewed to the right with a median of 0.4 field goal percentage.

The student government at a high school wants to conduct a survey of student opinion. It wants to begin with a simple random sample of 60 students. Which of the following survey methods will produce a simple random sample?

Number the students in the official school roster. Use a table of random numbers to choose 60 students from this roster for the survey.

Let random variable X represent the the number of visitors to a certain museum during a given day. The following table shows the probability distribution of the random variable. Which of the following claims about the distribution of random variable X is best supported by the histogram?

On a given day, it is equally likely for the museum to have less than 300 visitors as it is to have more than 300 visitors.

The following frequency table shows the responses from a group of college students who were asked to choose their favorite flavor of ice cream. Which of the following statements is not supported by the table?

One-half of the students chose vanilla or chocolate.

The continuous random variable N has a normal distribution with mean 7.5 and standard deviation 2.5. For which of the following is the probability equal to 0 ?

P(N = 8)

The following list shows the number of video games sold at a game store each day for one week. 15, 43, 50, 39, 22, 16, 20 Which of the following is the best classification of the data in the list?

Quantitative and discrete

At a large corporation, 6,000 employees from department A and 4,000 employees from department B are attending a training session. A random sample of 500 employees attending the session will be selected. Consider two sampling methods: with replacement and without replacement. How will the methods affect the standard deviations of the sampling distribution of the sample proportion of employees from department B?

Sampling WITHOUT replacement will result in a standard deviation LESS THAN but close to 0.4(0.6)500−−−−−√0.4(0.6)500.

A bank surveyed all of its 60 employees to determine the proportion who participate in volunteer activities. Which of the following statements is true?

The bank does not need to use an inference procedure to determine the proportion of employees who participate in volunteer activities because the survey was a census of all employees.

Researchers working for a certain airline are investigating the weight of carry-on bags. The researchers will use the mean weight of a random sample of 800 carry-on bags to estimate the mean weight of all carry-on bags for the airline. Which of the following best describes the effect on the bias and the variance of the estimator if the researchers increase the sample size to 1,300 ?

The bias will remain the same and the variance will decrease.

Which of the following is not a condition for constructing a confidence interval to estimate the difference between two population proportions?

The data must come from populations with approximately normal distributions.

Based on records kept at a gas station, the distribution of gallons of gas purchased by customers is skewed to the right with mean 10 gallons and standard deviation 4 gallons. A random sample of 64 customer receipts was selected, and the sample mean number of gallons was recorded. Suppose the process of selecting a random sample of 64 receipts and recording the sample mean number of gallons was repeated for a total of 100 samples. Which of the following is the best description of a dotplot created from the 100 sample means?

The dotplot is approximately normal with mean 10 gallons and standard deviation 0.5 gallon.

A large school district held a district-wide track meet for all high school students. For the 2-mile run, the population of female students participating had a mean running time of 8.8 minutes with standard deviation of 3.3 minutes, and the population of male students participating had a mean running time 7.3 minutes with standard deviation of 2.9 minutes. Suppose 8 female students and 8 male students who participated in the 2-mile run are selected at random from each population. Let x¯Fx¯F represent the sample mean running time for the female students, and let x¯Mx¯M represent the sample mean running time for the male students. What are the mean and standard deviation of the sampling distribution of the difference in sample means x¯F−x¯Mx¯F−x¯M ?

The mean is 1.5, and the standard deviation is (^2+^2)

The following relative frequency table shows the political party affiliation for a sample of 500 people in a certain town. Which of the following statements is supported by the table?

The number of people affiliated with the Independents is 100.

maria two routes commuting to work railroad crossing trains

The p-value is greater than a, and the null hypothesis is not rejected. There is not convincing evidence to support the claim that the proportion of times she needs to stop at the crossing is different for the different routes.

A recent survey indicated that the mean time spent on a music streaming service is 210 minutes per week for the population of a certain country. A simulation was conducted to create a sampling distribution of the sample mean for a population with a mean of 210. The following histogram shows the results of the simulation. Which of the following would be the best reason why the simulation of the sampling distribution is not approximately normal?

The sample size was not sufficiently large.

According to data from the United States Elections Project, only 36 percent of eligible voters voted in the 2014 elections. For random samples of size 40, which of the following best describes the sampling distribution of pˆ, the sample proportion of people who voted in the 2014 elections?

The sampling distribution is approximately normal, with mean 0.36 and standard deviation 0.076. A

A group of 80 people who had been diagnosed as prediabetic because of high blood glucose levels volunteered to participate in a study designed to investigate the use of cinnamon to reduce blood glucose to a normal level. Of the 80 people, 40 were randomly assigned to take a cinnamon tablet each day and the other 40 were assigned to take a placebo each day. The people did not know which tablet they were taking. Their blood glucose levels were measured at the end of one month. The results showed that 14 people in the cinnamon group and 10 people in the placebo group had normal blood glucose levels. For people similar to those in the study, do the data provide convincing statistical evidence that the proportion who would be classified as normal after one month of taking cinnamon is greater than the proportion who would be classified as normal after one month of not taking cinnamon?

There is not convincing statistical evidence at any reasonable significance level.

A one-sided hypothesis test is to be performed with a significance level of 0.05. Suppose that the null hypothesis is false. If a significance level of 0.01 were to be used instead of a significance level of 0.05, which of the following would be true? A Neither the probability of a Type II error nor the power of the test would change. B Both the probability of a Type II error and the power of the test would decrease. C Both the probability of a Type II error and the power of the test would increase. D The probability of a Type II error would decrease and the power of the test would increase. E The probability of a Type II error would increase and the power of the test would decrease.

e

A study was conducted to investigate whether a new drug could significantly reduce pain in people with arthritis. From a group of 500 people with arthritis, 250 were randomly assigned to receive the drug (group 1) and the remaining people were assigned a placebo (group 2). After one month of treatment, 225 people in group 1 reported pain relief and 150 people in group 2 reported pain relief. Let pˆC represent the combined (or pooled) sample proportion for the two samples. Have the conditions for inference for testing the difference in population proportions been met? A No. The people in the study were not selected at random. B No. The number of people in the study was too large compared with the size of the population. C No. The normality of the sampling distribution cannot be assumed because pˆC times each sample size is not sufficiently large. D No. The normality of the sampling distribution cannot be assumed because 1−pˆC times each sample size is not sufficiently large. E Yes. All conditions for inference have been met.

e

Which of the following graphs represents a binomial distribution with n = 20 and p = 0.25?

highest at five

Which of the following pairs of sample size n and population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion p̂?

n = 100 and p close to 1/2

Approximately 52 percent of all recent births were boys. In a simple random sample of 100 recent births, 49 were boys and 51 were girls. The most likely explanation for the difference between the observed results and the expected results in this case is

variability due to sampling. B

According to a recent survey, 81 percent of adults in a certain state have graduated from high school. If 15 adults from the state are selected at random, what is the probability that 5 of them have not graduated from high school?

(515​)(0.19)5(0.81)10

The mean number of pets owned by the population of students at a large high school is 3.2 pets per student with a standard deviation of 1.7 pets. A random sample of 16 students will be selected and the mean number of pets for the sample will be calculated. What is the mean of the sampling distribution of the sample mean for samples of size 16 ?

3.2

The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachael is at the 99th percentile in height for adult women, then her height, in inches, is closest to

70

At a certain clothing store, the clothes are displayed on racks. The clothes on each rack have similar prices, but the prices among the racks are very different. To estimate the typical price of a single piece of clothing, a consumer will randomly select four pieces of clothing from each rack. What type of sample is the consumer selecting?

A stratified random sample

Which of the following is the best description of a positive association between two variables?

As the value of one of the variables increases, the value of the other variable tends to increase.

A market researcher asked a group of men and women to choose their favorite color design from a sample of advertisements. The results are shown in the following table. Which of the following statements is not supported by the table?

For men, the number who chose a design with black was greater than the number who chose a design with blue.

randomized experiments particular drug certain disease anticipated

I, II, and III

The following pie chart summarizes the results of a survey given to airlines about the primary reason for flight delays. Which of the following statements is supported by the pie chart?

More delays were caused by weather than by all other reasons combined.

The height hh and collar size cc, both in centimeters, measured from a sample of boys were used to create the regression line cˆ=−94+0.9hc^=−94+0.9h. The line is used to predict collar size from height, both in centimeters, for boys' shirt collars. Which of the following has no logical interpretation in context?

The c-intercept of the regression line

Which of the following conditions will create a biased estimator of a population parameter?

The expected value of the estimator is not equal to the population parameter.

If a probability distribution is symmetric, which of the following statements must be true?

The mean of the distribution is equal to the median of the distribution.

A survey was conducted to determine what percentage of college seniors would have chosen to attend a different college if they had known then what they know now. In a random sample of 100 seniors, 34 percent indicated that they would have attended a different college. A 90 percent confidence interval for the percentage of all seniors who would have attended a different college is A 24.7% to 43.3% B 25.8% to 42.2% C 26.2% to 41.8% D 30.6% to 37.4% E 31.2% to 36.8%

c

Market researchers interviewed a random sample of 60 men and a random sample of 55 women about their preferences for different color designs for the packaging of a certain product. Of those interviewed, 23 men and 28 women preferred color design X. Which of the following is the correct test statistic for a two-sample z-test for a difference in population proportions for men and women (men minus women) in their preference for color design X ?

z=(0.44)(0.56)(551​+601​)​0.38−0.51​

For a random sample of 20 professional athletes, there is a strong, linear relationship between the number of hours they exercise per week and their resting heart rate. For the athletes in the sample, those who exercise more hours per week tend to have lower resting heart rates than those who exercise less. Which of the following is a reasonable value for the correlation between the number of hours athletes exercise per week and their resting heart rate?

−0.87

Circuit boards are assembled by selecting 4 computer chips at random from a large batch of chips. In this batch of chips, 90 percent of the chips are acceptable. Let X denote the number of acceptable chips out of a sample of 4 chips from this batch. What is the least probable value of X?

0

The distribution of time needed to complete a certain programming task is approximately normal, with mean 47 minutes and standard deviation 6 minutes. Which of the following is closest to the probability that a randomly chosen task will take less than 34 minutes or more than 60 minutes to complete?

0.0303

Carly commutes to work, and her commute time is dependent on the weather. When the weather is good, the distribution of her commute times is approximately normal with mean 20 minutes and standard deviation 2 minutes. When the weather is not good, the distribution of her commute times is approximately normal with mean 30 minutes and standard deviation 4 minutes. Suppose the probability that the weather will be good tomorrow is 0.9. Which of the following is closest to the probability that Carly's commute time tomorrow will be greater than 25 minutes?

0.0950

A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. The reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. Suppose the reported values are the true mean and standard deviation for the population of subjects in the study. If a random sample of 144 subjects is selected from the population, what is the approximate probability that the mean of the sample will be more than 11.0 seconds?

0.2743. B

Scientists working for a water district measure the water level in a lake each day. The daily water level in the lake varies due to weather conditions and other factors. The daily water level has a distribution that is approximately normal with mean water level of 84.07 feet. The probability that the daily water level in the lake is at least 100 feet is 0.064. Which of the following is closest to the probability that on a randomly selected day the water level in the lake will be at least 90 feet?

0.29

A researcher in Alaska measured the age (in months) and the weight (in pounds) of a random sample of adolescent moose. When the least-squares regression analysis was performed, the correlation was 0.59. Which of the following is the correct way to label the correlation?

0.59

An experiment was conducted in which planks of wood painted red and green were shown to pigeons to investigate a pigeon's ability to select a certain color. Pigeons could accurately select the color of the plank of wood 20 percent of the time. A simulation was conducted in which a trial consisted of a pigeon being shown eight planks of wood and its number of successes being recorded. This process was repeated many times, and the results are shown in the histogram. Based on the results of the simulation, which of the following is closest to the probability that there were at most three successes in a trial?

0.94

The following table shows the probability distribution for the number of books a student typically buys at the annual book fair held at an elementary school. Number of Books01234567Probability0.350.200.150.100.070.080.040.01 Let the random variable B represent the number of books a student buys at the next book fair. What is the expected value of B?

1.79

Ten percent of all Dynamite Mints candies are orange and 45 percent of all Holiday Mints candies are orange. Two independent random samples, each of size 25, are selected - one from Dynamite Mints candies and the other from Holiday Mints candies. The total number of orange candies in the two samples is observed. What are the expected total number of orange candies and the standard deviation for the total number of orange candies, respectively, in the two samples?

13.75 and 2.905

The normal curve shown represents the sampling distribution of a sample mean for sample size n = 25, selected at random from a population with standard deviation σx.

15. C

A random sample of 374 United States pennies was collected, and the age of each penny was determined. According to the boxplot below, what is the approximate interquartile range (IQR) of the ages?

16

machine is used to fill bags with a popular brand of trail mix. The machine is calibrated so the distribution of the weights of the bags of trail mix is normal, with mean 240 grams and standard deviation 3 grams. Of the following, which is the least weight of a bag in the top 5 percent of the distribution?

234 grams

The distribution of lengths of salmon from a certain river is approximately normal with standard deviation 3.5 inches. If 10 percent of salmon are longer than 30 inches, which of the following is closest to the mean of the distribution?

26 inches

A box contains 10 tags, numbered 1 through 10, with a different number on each tag. A second box contains 8 tags, numbered 20 through 27, with a different number on each tag. One tag is drawn at random from each box. What is the expected value of the sum of the numbers on the two selected tags?

29.0

The random variable W has a geometric distribution with p = 0.25. Approximately how far do the values of W typically vary, on average, from the mean of the distribution?

3.46

A researcher studying a specific type of tree creates a least-squares regression line for relating the height and the diameter, both in meters, of a fully grown tree. The results are shown in the following computer output. Which of the following values represents the predicted change in the height of the tree for each one-meter increase in the diameter of the tree?

30

The following boxplot shows the typical gas mileage, in miles per gallon, for 20 different car models. Based on the boxplot, the top 25 percent of the cars have a typical gas mileage of at least how many miles per gallon?

35

A split ticket is a voting pattern in which a voter casts votes for candidates from more than one political party. In a recent study, 1,000 men and women were asked whether they voted a split ticket in the last election. The totals are shown in the following table. What value of aa would indicate no association between gender and voting pattern for the people in the sample?

480

The normal curve shown represents the sampling distribution of a sample mean for sample size n = 25, selected at random from a population with standard deviation \sigma_xσx​ Which of the following is the best estimate of the standard deviation of the population, \sigma_xσx​?

75

A manufacturer makes lightbulbs and claims that their reliability is 98 percent. Reliability is defined to be the proportion of nondefective items that are produced over the long term. If the company's claim is correct, what is the expected number of nondefective lightbulbs in a random sample of 1,000 bulbs?

980

The manager of a public swimming pool wants to compare the effectiveness of two laundry detergents, Detergent A and Detergent B, in cleaning the towels that are used daily. As each dirty towel is turned in, it is placed into the only washing machine on the premises. When the washing machine contains 20 towels, the manager flips a coin to determine whether Detergent A or Detergent B will be used for that load. The cleanliness of the load of towels is rated on a scale of 1 to 10 by a person who does not know which detergent was used. The manager continues this experiment for many days. Which of the following best describes the manager's study?

A completely randomized design

A study will be conducted to investigate whether there is a difference in pain relief for two brands of headache pills, N and P. Participants will be randomly assigned to one of two groups. One group will take pill N when they experience a headache, and the other group will take pill P when they experience a headache. Each participant will record the number of minutes it takes until relief from the headache is felt. The mean number of minutes will be calculated for each group. Which of the following is the appropriate test for the study?

A two-sample t-test for a difference between population means

Zoologists studying two populations of tigers conducted a two-sample t-test for the difference in means to investigate whether the tigers in population X weigh more, on average, than the tigers in population Y. Two independent random samples were taken, and the difference between the sample means was calculated. All conditions for inference were met, and the test produced a p-value of 0.02. Which of the following is a correct interpretation of the p-value?

Assuming that the mean weights for populations X and Y are equal, the probability of observing a difference as great or greater than the sample difference is 0.02.

In a study to determine whether miles driven is a good predictor of trade-in value, 11 cars of the same age, make, model, and condition were randomly selected. The following scatterplot shows trade-in value and mileage for those cars. Five of the points are labeled A, B, C, D, and E, respectively.

E

Which of the following does not describe a sampling method that has a potential source of voluntary response bias for the administration of a survey about college athletics at a university?

Giving the survey to 30 students selected at random from each of the eight dorms on campus

Let random variable Y represent the number of interviews conducted for job openings at a certain company. The following table shows the cumulative probability distribution of the discrete random variable Y. yP(Y<=y)5060.270.480.690.8101.0 Khaleed claims that the distribution of Y is skewed to the left with mean equal to 8 interviews. Is Khaleed's claim correct?

No, the distribution is uniform with mean equal to 8 interviews.

The distribution of age for players of a certain professional sport is strongly skewed to the right with mean 26.8 years and standard deviation 4.2 years. Consider a random sample of 4 players and a different random sample of 50 players from the population. Which of the following statements is true about the sampling distributions of the sample mean ages for samples of size 4 and samples of size 50 ?

Only the sampling distribution for size 50 will be approximately normal, and the mean for both will be 26.8.

The following graphs show the sampling distributions for two different point estimators, R and W, of the same population parameter. Which of the following statements is true?

R is biased, and W is unbiased.

A school nutritionist was interested in how students at a certain school would feel after taking a nutritional supplement. The nutritionist selected a random sample of twenty students from the school to participate in the study. Participants were asked to keep a journal on how well they felt after taking the supplement each day. What possible source of bias is present in the method of data collection?

Response bias where responses are self-reported

At a large corporation, 6,000 employees from department A and 4,000 employees from department B are attending a training session. A random sample of 500 employees attending the session will be selected. Consider two sampling methods: with replacement and without replacement. How will the methods affect the standard deviations of the sampling distribution of the sample proportion of employees from department B?

Sampling without replacement will result in a standard deviation less than but close to 0.4(0.6)500.5000.4(0.6)​​.

A family would like to build a linear regression equation to predict the amount of grain harvested per acre of land on their farm. They subdivide their land into several smaller plots of land for testing and would like to select an explanatory variable they can control. Which of the following is an appropriate explanatory variable that the family could use to create a linear regression equation?

The amount of fertilizer applied to each plot of land

Researchers working for a certain airline are investigating the weight of carry-on bags. The researchers will use the mean weight of a random sample of 800 carry-on bags to estimate the mean weight of all carry-on bags for the airline. Which of the following best describes the effect on the bias and the variance of the estimator if the researchers increase the sample size to 1,300 ?

The bias will remain the same and the variance will decrease. C

In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

The centers will ROUGHLY BE EQUAL, and the variability of simulation A will be LESS than the variability of simulation B.

A manufacturing company uses two different machines, A and B, each of which produces a certain item part. The number of defective parts produced by each machine is about 1 percent. Suppose two independent random samples, each of size 100, are selected, where one is a sample of parts produced by machine A and the other is a sample of parts produced by machine B. Which of the following is true about the sampling distribution of the difference in the sample proportions of defective parts?

The mean is 0 and the distribution will not be approximately normal.

A bag contains chips of which 27.5 percent are blue. A random sample of 5 chips will be selected one at a time and with replacement. What are the mean and standard deviation of the sampling distribution of the sample proportion of blue chips for samples of size 5 ?

The mean is 0.275, and the standard deviation is −√0.275(0.725)/5

A political scientist claims that negative advertising on television affects younger voters more than it affects older voters. To test this claim, the scientist obtained data from two random samples of voters categorized into two age-groups, older and younger. The null hypothesis was that there was no difference in the proportions of voters in the two age-groups who would be affected by negative ads. The alternative hypothesis was that the proportion of younger voters affected would be greater than the proportion of older voters affected. Assuming all conditions for inference were met, the scientist conducted the test at a significance level of α=0.05α=0.05. The resulting p-value was 0.206. Which of the following is the correct decision for the test?

The p-value is greater than \(\alpha)\, and the null hypothesis is not rejected. There is not convincing evidence to support the claim that younger voters are more affected by negative ads than are older voters.

Mr. Ikeler conducted a study investigating the effectiveness of a new method for teaching a mathematics unit. He recruited 80 students at a college and randomly assigned them to two groups. Group 1 was taught with the new method, and group 2 was taught with the traditional method. Both groups were taught by the same teacher. At the end of the unit, an achievement test was administered and used to make a comparison of the two groups. What is the response variable in the study?

The score on the achievement test

In the states of Florida and Colorado, veterinarians investigating obesity in dogs obtained random samples of pet medical records and recorded the weights of the dogs in the samples. A test was conducted of H0 : p1 = p2 versus Ha : p1 ≠ p2, where p1 represents the proportion of all overweight dogs in Florida and p2 represents the proportion of all overweight dogs in Colorado. The resulting test statistic for a two-sample z-test for a difference between proportions was 1.85. At the significance level α = 0.05, which of the following is a correct conclusion?

There is not sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the p-value is greater than 0.05.

An engineer believes that there is a linear relationship between the thickness of an air filter and the amount of particulate matter that gets through the filter; that is, less pollution should get through thicker filters. The engineer tests many filters of different thickness and fits a linear model. If a linear model is appropriate, what should be apparent in the residual plot?

There should be no pattern in the residual plot.

At a photography contest, entries are scored on a scale from 1 to 100. At a recent contest with 1,000 entries, a score of 68 was at the 77th77th percentile of the distribution of all the scores. Which of the following is the best description of the 77th77th percentile of the distribution?

There were 770 entries with a score less than or equal to 68.

Researchers were investigating whether there is a significant difference between two medications, R and S, designed to reduce fleas found on cats. From a sample of 300 cat owners, the researchers randomly assigned 150 cat owners to use medication R on their cats and the remaining cat owners to use medication S. For the cats using medication R, 88 percent had no fleas. For the cats using medication S, 90 percent had no fleas. Which of the following is the most appropriate method for analyzing the results? A A two-sample z-test for a difference in population proportions B A two-sample z-test for a difference in sample proportions C A one-sample z-test for a sample proportion D A one-sample z-test for a population proportion E A one-sample z-test for a difference in sample proportions

a

A sample of size n will be selected from a population with population proportion p. Which of the following must be true for the sampling distribution of the sample proportion to be approximately normal?

a. Both np and n(1−p) are at least 10.

For which of the following is the shape of the sampling distribution of the sample mean approximately normal? A random sample of size 5 from a population that is approximately normal A random sample of size 10 from a population that is strongly skewed to the right A random sample of size 60 from a population that is strongly skewed to the left

a. I only

A marketing company wants to estimate the proportion of consumers in a certain region of the country who would react favorably to a new marketing campaign. Further, the company wants the estimate to have a margin of error of no more than 5 percent with 90 percent confidence. Of the following, which is closest to the minimum number of consumers needed to obtain the estimate with the desired precision? A 136 B 271 C 385 D 542 E 769

b

The mean number of pets owned by the population of students at a large high school is 3.2 pets per student with a standard deviation of 1.7 pets. A random sample of 16 students will be selected and the mean number of pets for the sample will be calculated.

b. 3.2

The histograms show the results of three simulations of a sampling distribution of a sample mean. For each simulation, 1,500 samples of size n were selected from the same population and the sample mean was recorded. The value of n was different for each of the three simulations. Which of the following is the correct ordering of the graphs from least value of n to greatest value of n ?

A, C, B

George and Michelle each claimed to have the better recipe for chocolate chip cookies. They decided to conduct a study to determine whose cookies were really better. They each baked a batch of cookies using their own recipe. George asked a random sample of his friends to taste his cookies and to complete a questionnaire on their quality. Michelle asked a random sample of her friends to complete the same questionnaire for her cookies. They then compared the results. Which of the following statements about this study is false?

Because George and Michelle used the same questionnaire, their results will generalize to the combined population of their friends.

A soda manufacturer claims that its Cherry Fizz soda has more carbonation than a competitor's Cherry Eclipse soda. Bottles of both types of soda are opened, covered with a balloon, and then shaken. The diameter of each balloon is then measured. The mean balloon diameters are 2.3 inches for the Cherry Fizz soda and 2.1 inches for the Cherry Eclipse soda. A 90 percent confidence interval to estimate the difference in mean diameters, in inches, is ( -0.8, 1.2 ) Which of the following claims is supported by the interval?

Because the interval contains 0, it is possible that there is no difference in mean carbonation levels.

A sample of size n will be selected from a population with population proportion p. Which of the following must be true for the sampling distribution of the sample proportion to be approximately normal?

Both np and n(1 - p) are at least 10

A sample of size nn will be selected from a population with population proportion pp. Which of the following must be true for the sampling distribution of the sample proportion to be approximately normal?

Both np and n(1−p) are at least 10.

The distribution of prices for a certain car model is approximately normal with mean $21,800 and standard deviation $400. A random sample of 4 cars of the model will be selected. What is the correct unit of measure for the mean of the sampling distribution of \overline{x}?x?

Dollars

The distribution of prices for a certain car model is approximately normal with mean $21,800 and standard deviation $400. A random sample of 4 cars of the model will be selected. What is the correct unit of measure for the mean of the sampling distribution of x¯x¯ ?

Dollars

Two non-profit organizations, L and M, accept donations from people. In a certain month, 140 people donated to organization L, with an average donation amount of x¯L=$113x¯L=$113, and 42 people donated to organization M, with an average donation amount of x¯M=$390x¯M=$390. What is the correct unit of measure for the mean of the sampling distribution of x¯L−x¯Mx¯L−x¯M?

Dollars

Two non-profit organizations, L and M, accept donations from people. In a certain month, 140 people donated to organization L, with an average donation amount of x‾L=$113,xL​=$113, and 42 people donated to organization M, with an average donation amount of x‾M=$390.xM​=$390. What is the correct unit of measure for the mean of the sampling distribution of x‾L−x‾M?xL​−xM​?

Dollars

The least-squares regression line Sˆ=0.5+1.1LS^=0.5+1.1L models the relationship between the listing price and the actual sales price of 12 houses, with both amounts given in hundred-thousands of dollars. Let LL represent the listing price and SS represent the sales price. Which of the following is the best interpretation of the slope of the regression line?

E For each hundred-thousand-dollar increase in the listing price, the sales price is predicted to increase by $110,000.

A two-sample t-test for a difference in means was conducted to investigate whether defensive players on a football team can bench-press more weight, on average, than offensive players. The conditions for inference were met, and the test produced a test statistic of t = 1.083 and a p-value of 0.15. Based on the p-value and a significance level of α=0.05α=0.05 which of the following is the correct conclusion?

Fail to reject the null hypothesis because 0.15 > 0.05. There is not convincing evidence that defensive players can bench-press more weight, on average, than offensive players.

Consider a situation in which sampling without replacement is used to generate a random sample from each of two separate populations. To calculate a confidence interval to estimate the difference between population proportions, which of the following checks must be made?

Each population must be at least 10 times as large as its corresponding sample.

A botanist found a correlation between the length of an aspen leaf and its surface area to be 0.94. Why does the correlation value of 0.94 not necessarily indicate that a linear model is the most appropriate model for the relationship between length of an aspen leaf and its surface area?

Even with a correlation value of 0.94, it is possible that the relationship could still be better represented by a nonlinear model.

In the states of Florida and Colorado, veterinarians investigating obesity in dogs obtained random samples of pet medical records and recorded the weights of the dogs in the samples. A test was conducted of H0 : p1= p2 versus Ha : p1 ≠ p2, where p1 represents the proportion of all overweight dogs in Florida and p2 represents the proportion of all overweight dogs in Colorado. The resulting test statistic for a two-sample z-test for a difference between proportions was 1.85. At the significance level α = 0.05, which of the following is a correct conclusion? A There is not sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the p-value is greater than 0.05. B There is not sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the z-test statistic is greater than 0.05. C There is sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the p-value is greater than 0.05. D There is sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the p-value is less than 0.05. E There is sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is greater than the proportion of all overweight dogs in Colorado because the z-test statistic is positive.

a

Clara recorded 50 numerical observations on a certain variable and then calculated the mean x¯ and the standard deviation s for the observations. To help decide whether a normal model is appropriate, she created the following chart.

a. 1, 7, 34, 7, 1

A medical doctor uses a diagnostic test to determine whether a patient has arthritis. A treatment will be prescribed only if the doctor thinks the patient has arthritis. The situation is similar to using a null and an alternative hypothesis to decide whether to prescribe the treatment. The hypotheses might be stated as follows. H0 : The patient does not have arthritis Ha : The patient has arthritis Which of the following represents a Type II error for the hypotheses? A Diagnosing arthritis in a patient who has arthritis B Failing to diagnose arthritis in a patient who has arthritis C Diagnosing arthritis in a patient who does not have arthritis D Failing to diagnose arthritis in a patient who does not have arthritis E Prescribing treatment to a patient regardless of the diagnosis

b

Based on a survey of a random sample of 900 adults in the United States, a journalist reports that 60 percent of adults in the United States are in favor of increasing the minimum hourly wage. If the reported percent has a margin of error of 2.7 percentage points, which of the following is closest to the level of confidence? A 80.0% B 90.0% C 95.0% D 95.5% E 99.0%

b

Consider the results of a hypothesis test, which indicate there is not enough evidence to reject the null hypothesis. Which of the following statements about error is correct? A A Type I error could have been made, but not a Type IIerror. B A Type II error could have been made, but not a Type Ierror. C Both types of error could have been made, but the probability of a Type I error is greater than the probability of a Type II error. D Both types of error could have been made, but the probability of a Type I error is less than the probability of a Type II error. E The type of error that could have been made is not possible to determine without knowing the statement of the null hypothesis.

b

For a certain population of sea turtles, 18 percent are longer than 6.5 feet. A random sample of 90 sea turtles will be selected. What is the standard deviation of the sampling distribution of the sample proportion of sea turtles longer than 6.5 feet for samples of size 90 ?

b

From a random sample of potential voters in an upcoming election, 47% indicated they intended to vote for Candidate R. A 95 percent confidence interval was constructed from the sample, and the margin of error for the estimate was 5%. Which of the following is the best interpretation of the interval? A We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is between 42% and 52%. B We are 95% confident that the proportion who intend to vote for Candidate R from the population is between 42% and 52%. C We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is 47%. D We are 95% confident that the proportion who intend to vote for Candidate R from the population is 47%. E We are confident that 95% of the population intend to vote for Candidate R.

b

On the day before an election in a large city, each person in a random sample of 1,000 likely voters is asked which candidate he or she plans to vote for. Of the people in the sample, 55 percent say they will vote for candidate Taylor. A margin of error of 3 percentage points is calculated. Which of the following statements is appropriate? A The proportion of all likely voters who plan to vote for candidate Taylor must be the same as the proportion of voters in the sample who plan to vote for candidate Taylor (55 percent), because the data were collected from a random sample. B The sample proportion minus the margin of error is greater than 0.50, which provides evidence that more than half of all likely voters plan to vote for candidate Taylor. C It is not possible to draw any conclusion about the proportion of all likely voters who plan to vote for candidate Taylor because the 1,000 likely voters in the sample represent only a small fraction of all likely voters in a large city. D It is not possible to draw any conclusion about the proportion of all likely voters who plan to vote for candidate Taylor because this is not an experiment. E It is not possible to draw any conclusion about the proportion of all likely voters who plan to vote for candidate Taylor because this is a random sample and not a census.

b

Suppose that 25 percent of women and 22 percent of men would answer yes to a particular question. In a simulation, a random sample of 100 women and a random sample of 100 men were selected, and the difference in sample proportions of those who answered yes, p̂women - p̂men, was calculated. The process was repeated 1,000 times. Which of the following is most likely to be a representation of the simulated sampling distribution of the difference between the two sample proportions?

b

The distribution of time needed to complete a certain programming task is approximately normal, with mean 47 minutes and standard deviation 6 minutes. Which of the following is closest to the probability that a randomly chosen task will take less than 34 minutes or more than 60 minutes to complete?

b. 0.0303

A company that ships glass for a glass manufacturer claimed that its shipping boxes are constructed so that no more than 8 percent of the boxes arrive with broken glass. The glass manufacturer believed the actual percent is greater than 8 percent. The manufacturer selected a random sample of boxes and recorded the proportion of boxes that arrived with broken glass. The manufacturer tested the hypotheses H0:p=0.08 versus Ha:p>0.08 at the significance level of α=0.01. The test yielded a p-value of 0.001. Assuming all conditions for inference were met, which of the following is the correct conclusion? A The p-value is greater than α, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08. B The p-value is greater than α, and the null hypothesis is rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08. C The p-value is greater than α, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08. D The p-value is less than α, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08. E The p-value is less than α, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.

d

A factory manager selected a random sample of parts produced on an old assembly line and a random sample of parts produced on a new assembly line. The difference between the sample proportion of defective parts made on the old assembly line and the sample proportion of defective parts made on the new assembly line (old minus new) was 0.006. Under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being the proportion of defective parts made on the old assembly line is greater than that of the new assembly line. The p-value of the test was 0.018. Which of the following is the correct interpretation of the p-value? A If there is a difference of 0.018 in the proportions of all defective parts made on the two assembly lines, the probability of observing that difference is 0.006. B If there is a difference of 0.006 in the proportions of all defective parts made on the two assembly lines, the probability of observing that difference is 0.018. C If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference equal to 0.006 is 0.018. D If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference of at least 0.006 is 0.018. E If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference of at most 0.006 is 0.018.

d

A one-sample z-test for a population proportion will be conducted using a simple random sample selected without replacement from a population. Which of the following is a check for independence? A np0≥10 and n(1−p0)≥10 for sample size n and population proportion p0. B Each sample proportion value is less than or equal to 0.5. C The sample size is more than 10 times the population size. D The population size is more than 10 times the sample size. E The population distribution is approximately normal.

d

Dan selected a random sample of 100 students from the 1,200 at his school to investigate preferences for making up school days lost due to emergency closings. The results are shown in the table below. Dan incorrectly performed a large sample test of the difference in two proportions using 58/100 and 42/100 and calculated a p-value of 0.02. Consequently, he concluded that there was a significant difference in preference for the two options. Which of the following best describes his error in the analysis of these data? A No statistical test was necessary because 0.58 is clearly larger than 0.42. B The results of the test were invalid because less than 10% of the population was sampled. C Dan performed a two-tailed test and should have performed a one-tailed test. D A one-sample test for a proportion should have been performed because only one sample was used. E More options should have been included, and a chi-square test should have been performed.

d

Elly and Drew work together to collect data to estimate the percentage of their classmates who own a particular brand of shoe. Using the same data, Elly will construct a 90 percent confidence interval and Drew will construct a 99 percent confidence interval. Which of the following statements is true? A The midpoint of Elly's interval will be greater than the midpoint of Drew's interval. B The midpoint of Elly's interval will be less than the midpoint of Drew's interval. C The width of Elly's interval will be greater than the width of Drew's interval. D The width of Elly's interval will be less than the width of Drew's interval. E The width of Elly's interval will be equal to the width of Drew's interval.

d

In 2009 a survey of Internet usage found that 79 percent of adults age 18 years and older in the United States use the Internet. A broadband company believes that the percent is greater now than it was in 2009 and will conduct a survey. The company plans to construct a 98 percent confidence interval to estimate the current percent and wants the margin of error to be no more than 2.5 percentage points. Assuming that at least 79 percent of adults use the Internet, which of the following should be used to find the sample size (n) needed? A 1.96(0.5)n−−−−√≤0.025 B 1.96(0.5)(0.5)n−−−−−−√≤0.025 C 2.33(0.5)(0.5)n−−−−−−√≤0.05 D 2.33(0.79)(0.21)n−−−−−−−−√≤0.025 E 2.33(0.79)(0.21)n−−−−−−−−√≤0.05

d

Machines at a bottling plant are set to fill bottles to 12 ounces. The quality control officer at the plant periodically tests the machines to be sure that the bottles are filled to an appropriate amount. The null hypothesis of the test is that the mean is at least 12 ounces. The alternative hypothesis is that the mean is less than 12 ounces. Which of the following describes a Type I error that could result from the test? A The test does not provide convincing evidence that the mean is less than 12 ounces, but the actual mean is at least 12 ounces. B The test does not provide convincing evidence that the mean is less than 12 ounces, but the actual mean is less than 12 ounces. C The test does not provide convincing evidence that the mean is less than 12 ounces, but the actual mean is 12 ounces. D The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is at least 12 ounces. E The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is 11 ounces.

d