AP Statistics Midterm
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
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
Data will be collected on the following variables. Which variable can be considered discrete?
The number of books a person finished reading last month
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
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 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
The statistic x¯ is used as an estimator for which of the following?
μ
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 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 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.
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.
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
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.
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
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.
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)
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
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.
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
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 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.
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.
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.
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 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.
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.
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.
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
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
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
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 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.
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.
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
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
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
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
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.
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
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
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
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.
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
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
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
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.
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
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 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.
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.
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.
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.
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.
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.
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.
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 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.
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 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
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 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
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
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
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.
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.
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 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
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
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
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
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.
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.
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
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
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
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.
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.
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.
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 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.
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.
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.
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.
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 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
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
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.
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 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.
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.
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
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
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.
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
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.
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
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
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
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 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
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
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
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 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).
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
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 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
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
