AP Stats Midterm TQ

A researcher is studying a group of field mice. The distribution of the weight of field mice is approximately normal with mean 25 grams and standard deviation 4 grams. Which of the following is closest to the proportion of field mice with a weight greater than 33 grams?

0.023

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 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?

0.6

In a parking lot with 200 cars, 50 cars are white, 30 cars are red, and 20 cars are silver. One car will be selected at random from the parking lot. If each car in the parking has only one color, which of the following cannot be the probability that the selected car will be green?

0.6

At a sporting event, cheerleaders will throw 50 bundled T-shirts into the crowd. The T-shirt sizes consist of 10 small, 15 medium, and the remainder either large or extra large. Suppose Ana catches a T-shirt. What is the probability that she will catch a T-shirt that is not a size small?

0.80

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(square root 3.6)

A middle school chess club has 5 members: Adam, Bradley, Carol, Dave, and Ella. Two students from the club will be selected at random to participate in the county chess tournament. What is the probability that Adam and Ella will be selected?

1/10

For a certain online store, the distribution of number of purchases per hour is approximately normal with mean 1,200 purchases and standard deviation 200 purchases. For what proportion of hours will the number of purchases at the online store exceed 1,400 ?

16%

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

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 � 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 statistician at a metal manufacturing plant is sampling the thickness of metal plates. If an outlier occurs within a particular sample, the statistician must check the configuration of the machine. The distribution of metal thickness has mean 23.5 millimeters (mm) and standard deviation 1.4 mm. Based on the two-standard deviations rule for outliers, of the following, which is the greatest thickness that would require the statistician to check the configuration of the machine?

20.6

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 in

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

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

A market research firm is studying the effects of price and type of packaging on sales of a particular product. Twenty-seven stores with shoppers of similar characteristics will be used in the study. The nine combinations of three price levels and three packaging types are the treatments of interest. Total sales of the product over a seven-week period will be recorded. Which of the following describes the best design to use for the study?

A completely randomized design. Randomly assign the nine combinations of price level and packaging type so that three stores use each combination.

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 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 researcher selects a simple random sample of 1,200 women who are students at Midwestern colleges in the United States to use for an observational study. Which of the following describes the population to which it would be most reasonable to generalize the results?

All women who are students at Midwestern colleges in the United States

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=0.86. 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 store owner reports that the probability that a customer who purchases a lawn mower will also purchase an extended warranty is 0.68. Which of the following is the best interpretation of the probability 0.68 ?

For all customers who purchase a lawn mower, 68% will also purchase an extended warranty.

In a certain region, 94 percent of the people have a certain characteristic in their blood. Suppose a group of 45 people from the region are selected at random. Let the random variable � represent the number of people in the sample without the characteristic. Random variable � follows a binomial distribution with a mean of 2.7 people. Which of the following is the best interpretation of the mean?

For all groups of 45 people, the average number of people without the characteristic is 2.7.

A company that ships crystal bowls claims that bowls arrive undamaged in 95 percent of the shipments. Let the random variable � represent the number of shipments with undamaged bowls in 25 randomly selected shipments. Random variable � 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 least-squares regression line s^=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 L represent the listing price and S represent the sales price. Which of the following is the best interpretation of the slope of the regression line?

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

A fair die with its faces numbered from 1 to 6 will be rolled. Which of the following is the best interpretation of the probability that the number landing face up will be less than 3 ?

For many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 1/3

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), community college (CC), join the workforce (W), join the military (M), or undecided (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.

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 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? A

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

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

Joslyn performed an experiment using a die with its faces numbered from 1 to 6. She rolled the die and recorded whether the 5 landed face up. She repeated the process many times and kept a cumulative record of the total number of rolls and the total number of 5s landing face up. The following table shows part of her record. Suppose Joslyn could roll the die 10,000 times and keep a record of the total number of 5s landing face up in the 10,000 rolls. What would such a record illustrate?

Law of Large Numbers

Mateo plays on his school basketball team. From past history, he knows that his probability of making a basket on a free throw is 0.8. Suppose he wants to create a simulation using random numbers to estimate the probability of making at least 3 baskets on his next 5 free throw attempts. Which of the following assignments of the digits 0 to 9 could be used for the simulation?

Let the digits from 0 to 7 represent making a basket and the digits 8 and 9 represent not making a basket.

The probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0.40. Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey. Is Avery interpreting the probability correctly?

No, because 0.40 represents probability in the long run over many visits to the site.

Roger claims that the two statistics most likely to change greatly when an outlier is added to a small data set are the mean and the median. Is Roger's claim correct?

No, only the mean is likely to change greatly.

e 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.

The owner of a food store conducted a study to investigate whether displaying organic fruit at the front of the store rather than at the back of the store will increase sales of the fruit. At the beginning of each week, the organic fruit display was randomly assigned to either the front or the back of the store, and sales for the week were recorded. At the end of 12 months, the owner determined that the average weekly sales of organic fruit displayed at the front of the store were greater than the average weekly sales of organic fruit displayed at the back of the store. The difference was statistically significant. What can be concluded from the study?

Placing the display at the front instead of the back of the store causes an increase, on average, of weekly sales of the organic fruit.

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

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 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

The height ℎ and collar size c both in centimeters, measured from a sample of boys were used to create the regression line c^=−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 describes a continuous variable?

The diameters of the tree trunks at an evergreen farm

Researchers will use a well-designed experiment to test the effectiveness of a new drug versus a placebo in relieving symptoms of the common cold. Which of the following will provide evidence that the new drug causes relief of symptoms?

The difference between the responses to the new drug and the placebo must be shown to be statistically significant to provide evidence that the new drug causes relief.

Which of the following statements is true about a distribution that appears to have a gap when displayed as a histogram?

The distribution has a region between two data values where no data were observed.

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

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 � represents the number of chairs in a sample of chairs that are defective. The mean of � is 10 chairs and the standard deviation is 3 chairs. Based on the distribution of �, which of the following would be an accurate interpretation of the value 0.1 ?

The probability of identifying a defective chair

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

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.

The quality-control manager of a large factory is concerned about the number of defective items produced by workers. Thirty workers at the factory agree to participate in a study of three different incentive plans to help reduce the number of defective items produced. The plans will be randomly assigned to the workers so that 10 workers received each plan. The reduction in the number of defective items produced by each worker will be recorded two weeks after the plans are implemented. Which of the following best describes why a completely randomized design is an appropriate design to use in this situation?

There is no blocking variable, and incentive plans will be randomly assigned to the workers.

A chemist for a paint company conducted an experiment to investigate whether a new outdoor paint will last longer than the older paint. Fifty blocks made from the same wood were randomly assigned to be painted with either the new paint or the old paint. The blocks were placed into a weather-controlled room that simulated extreme weather conditions such as ice, temperature, wind, and sleet. After one month in the room, the blocks were removed, and each block was rated on texture, shine, brightness of color, and chipping. The results showed that the blocks painted with the new paint generally had higher ratings than the blocks painted with the old paint. However, an analysis of the results found that the difference in ratings was not statistically significant. What can be concluded from the experiment?

There is not enough evidence to attribute the higher ratings to the new paint.

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 77th percentile of the distribution of all the scores. Which of the following is the best description of the 77th percentile of the distribution?

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

Which of the following questions about cars in a school parking lot will allow for the collection of a set of categorical data?

What are the colors of the cars in the lot?

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

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?

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

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

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

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

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