AP Stat Semester 1 Exam

The histogram shown summarizes the responses of 100 people when asked, "What was the price of the last meal you purchased?" Based on the histogram, which of the following could be the interquartile range of the prices?

$5

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

A random sample of 1,092 people were asked whether color was a consideration in buying a new car. They were also asked to identify one additional feature that was important. The responses are shown in the table. Which of the following is closest to the proportion of people who responded no to color consideration and who identified safety as the additional feature that was important?

.18

A summer resort rents rowboats to customers but does not allow more than four people to a boat. Each boat is designed to hold no more than 800 pounds. Suppose the distribution of adult males who rent boats, including their clothes and gear, is normal with a mean of 190 pounds and standard deviation of 10 pounds. If the weights of individual passengers are independent, what is the probability that a group of four adult male passengers will exceed the acceptable weight limit of 800 pounds?

0.023

The probability that a new microwave oven will stop working in less than 2 years is 0.05. The probability that a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. The probability that a new microwave oven is damaged during delivery is 0.10. Given that a new microwave oven is damaged during delivery, what is the probability that it stops working in less than 2 years?

0.40

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 large store has a customer service department where customers can go to ask for help with store-related issues. According to store records, approximately ¼ of all customers who go to the service department ask for help finding an item. Assume the reason each customer goes to the service department is independent from customer to customer. Based on the approximation, what is the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item?

1-(3/4)^4

The amount of time required for each of 100 mice to navigate through a maze was recorded. The histogram below shows the distribution of times, in seconds, for the 100 mice. Which of the following values is closest to the standard deviation of the 100 times?

10 seconds

The following table shows data that were collected from a random sample of people, who indicated their age and their favorite sporting event to watch on television. Based on the results above, what proportion of the randomly sampled people are over age 12 years?

2,300/3500

An amusement park attraction has a sign that indicates that a person must be at least 48 inches tall to ride the attraction. The following boxplot shows the heights of a sample of people who entered the amusement park on one day. Based on the boxplot, approximately what percent of the people who entered the amusement park met the height requirement for the attraction?

50%

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 random sample of 25 households from the Mountainview School District was surveyed. In this survey, data were collected on the age of the youngest child living in each household. The histogram below displays the data collected in the survey. In which of the following intervals is the median of these data located?

8 years old to less than 10 years old

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 researcher is studying the effect of genetically modified (GM) and nongenetically modified (nGM) corn on the weight gain of lambs. The sex and genetics of the lambs can affect their weight gain. Five sets of male twin lambs and five sets of female twin lambs—for a total of twenty lambs—are available for the study. The lambs will be randomly assigned to a diet of either GM or nGM diet of corn. Weight gain will be recorded for each lamb after five weeks on the diet. Which of the following designs would be best to use in the study?

A matched pairs design. For each set of twins, randomly assign one twin to the GM diet and the other twin to the nGM diet.

At a large conference of teachers from a variety of subjects, a random sample of 50 mathematics teachers attending the conference was selected. Among the selected mathematics teachers, 28 percent had taken one or more courses in statistics. For which of the following populations is 28 percent a reasonable estimate of the percentage of those who have taken one or more courses in statistics?

All mathematics teachers who attended the conference

A company determines the mean and standard deviation of the number of sick days taken by its employees in one year. Which of the following is the best description of the standard deviation?

Approximately the mean distance between the number of sick days taken by individual employees and the mean number of sick days taken by all employees

In a recent poll of 1,500 randomly selected eligible voters, only 525 (35 percent) said that they did not vote in the last election. However, a vote count showed that 80 percent of eligible voters actually did not vote in the last election. Which of the following types of bias is most likely to have occurred in the poll?

Response bias

A large online retailer places packed and ready-to-be-shipped boxes in a line on a conveyor belt. A sample of boxes will be used to estimate the mean weight of boxes shipped on a given day. One proposed method for selecting the sample is as follows: Generate a random integer from 1 to 20. Use that integer to select an initial box from the first 20 boxes in line on the conveyor belt. Select every 25th box that follows the initial box on the conveyor belt for the rest of the day. Which of the following best describes the proposed sampling method?

Systematic random sample

An experiment will be conducted to determine whether children learn their multiplication facts better by practicing with flash cards or by practicing on a computer. Children who volunteer for the experiment will be randomly assigned to one of the two treatments. Because the children's gender may affect the outcome, there will be blocking by gender. After practice, the children will be given a test on their multiplication facts. Why will it be impossible to conduct a double-blind experiment?

The child will know whether he or she used flash cards or the computer.

The following dotplot shows the scores of 25 people who played an online trivia game. Which of the following statements is the best description of the distribution of scores?

The distribution is skewed right.

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.

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

The number of people affiliated with the Independents is 100.

Under which of the following conditions is it preferable to use stratified random sampling rather than simple random sampling?

The population can be divided into strata so that the individuals in each stratum are as much alike as possible.

Which of the following statements must be true about the data sets A and B displayed in the histograms above?

The standard deviation of data set A is greater than the standard deviation of data set B.

A graph (not shown) of the selling prices of homes in a certain city for the month of April reveals that the distribution is skewed to the left. Which of the following statements is the most reasonable conclusion about the selling prices based on the graph?

The value of maximum minus third quartile is less than the value of first quartile minus minimum.

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.

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?

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.

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 264.0 calories per day.

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.

A researcher conducting a telephone survey is concerned about possible sources of bias. Of the following, which is the best example of nonresponse bias?

Many of the people selected to participate in the survey who do not respond might have opinions different from those who do respond.

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. 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.

A randomized block design will be used in an experiment to compare two lotions that protect people from getting sunburned. Which of the following should guide the formation of the blocks?

Participants within each block should be as similar as possible with respect to how easily they get sunburned.

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

The following bar chart shows the relative frequency of days of rain for 30 days in four regions of a certain state. Which of the following statements is not supported by the bar chart?

Region C had more than 25 days of rain.

In a certain school, students can choose whether to eat in the school's cafeteria. A reporter working for the school's newspaper polled students on their reactions to changes in the menu at the cafeteria. For each student leaving the cafeteria in one 30-minute time period, the reporter used a coin to determine whether to stop the student and ask how he or she felt about the new menu. In the reporter's article it was stated that a random sample of the students showed that 89 percent of the school's student population was happy with the new menu. Which of the following statements is true?

Because students self-selected whether to eat in the cafeteria, the sampling method might be biased and the sample might not be representative of all students in the school.

A dog food company wishes to test a new high-protein formula for puppy food to determine whether it promotes faster weight gain than the existing formula for that puppy food. Puppies participating in an experiment will be weighed at weaning (when they begin to eat puppy food) and will be weighed at one-month intervals for one year. In designing this experiment, the investigators wish to reduce the variability due to natural differences in puppy growth rates. Which of the following strategies is most appropriate for accomplishing this?

Block on dog breed and randomly assign puppies to existing and new formula groups within each breed.

The following table shows the data collected from students in grades 3 and 4 in an elementary school about their favorite types of pets. Which of the following statements is supported by the table?

Dogs were the type of pet chosen most often by the students at the elementary school.

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. Which of the five labeled points is the most influential with respect to a regression of trade-in value versus miles driven?

E

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.

The SC Electric Company has bid on two electrical wiring jobs. The owner of the company believes that the probability of being awarded the first job (event A) is 0.75; the probability of being awarded the second job (event B) is 0.5; and the probability of being awarded both jobs (event (A and B)) is 0.375. If the owner's beliefs are correct, which of the following statements must be true concerning event A and event B ?

Event A and event B are not mutually exclusive and are independent.

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

Ming is learning the game of tennis and will practice serving a tennis ball within bounds. Assume that the probability of Ming serving a tennis ball within bounds is 0.40 and that her serves are independent of each other. What is the probability that the first time Ming serves a tennis ball within bounds will occur on her 4th attempt?

(0.6)^3 (0.4)

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?

(15 5) (0.19)^5 (0.81)^10

First-year students enrolled at a college were asked whether they play video games. The responses, classified by whether the students were enrolled in the school of sciences or the school of arts, are shown in the table. Of all the students enrolled in the school of arts who responded, approximately what proportion responded that they play video games?

.438

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

Joe and Matthew plan to visit a bookstore. Based on their previous visits to this bookstore, the probability distributions of the number of books they will buy are given below. Assuming that Joe and Matthew make their decisions independently, what is the probability that they will purchase no books on this visit to the bookstore?

0.1250

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 student is applying to two different agencies for scholarships. Based on the student's academic record, the probability that the student will be awarded a scholarship from Agency A is 0.55 and the probability that the student will be awarded a scholarship from Agency B is 0.40. Furthermore, if the student is awarded a scholarship from Agency A, the probability that the student will be awarded a scholarship from Agency B is 0.60. What is the probability that the student will be awarded at least one of the two scholarships?

0.62

The least-squares regression line y^⁢=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 x represents velocity and y represents the depth of the river. What is the predicted value of y, in feet, when x=5?

0.8

A police officer is using a radar device to check motorists' speeds. Prior to beginning the speed check, the officer estimates that 40 percent of motorists will be driving more than 5 miles per hour over the speed limit. Assuming that the police officer's estimate is correct, what is the probability that among 4 randomly selected motorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit?

0.8704

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

x y 1 3 2 4 3 7 4 8 5 12 The table shows several values of x and their corresponding values of y. Which of the following is closest to the correlation between x and y?

0.98

The distribution of monthly rent for one-bedroom apartments in a city is approximately normal with mean $936 and standard deviation $61. A graduate student is looking for a one-bedroom apartment and wants to pay no more than $800 in monthly rent. Of the following, which is the best estimate of the percent of one-bedroom apartments in the city with a monthly rent of at most $800 ?

1.3%

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. 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

A recent report indicated that 22 percent of the households in a certain community speak a language other than English at home. A reporter will randomly select a household from the community until the first household that speaks a language other than English at home is selected. Let random variable Q represent the number of attempts needed until the first household that speaks a language other than English at home is selected. The random variable Q has a geometric distribution with P=0.22. Which of the following is closest to the variance of the random variable?

16.1157

The number of hurricanes reaching the East Coast of the United States was recorded for each of the last ten decades by the National Hurricane Center. Summary measures are shown below. Min = 12 Max = 24 Lower quartile = 15 Upper quartile = 18 Median = 16 n = 10 Which of the following statements is true?

24 is an outlier and it is possible that there are other outliers at the high end of the data set. There are no outliers at the low end of the data set.

The seniors at three high schools were surveyed about their plans after graduation. The following table shows the responses, classified by high school. One senior from the high schools will be selected at random. What is the probability that the senior selected will not be from High School B given that the senior responded with a choice other than college?

396/538

The dotplot below displays the total number of miles that the 28 residents of one street in a certain community traveled to work in one five-day workweek. Which of the following is closest to the percentile rank of a resident from this street who traveled 85 miles to work that week?

70

Which of the following can be used to show a cause-and-effect relationship between two variables?

A controlled experiment

A car rental agency has two locations in a city. The boxplots below summarize the miles driven for one day of single-day car rentals at each location. Based on the boxplots, which statement provides the best comparison of the two locations?

Compared with location A, the miles driven for location B display more variability, and the median is greater.

A company that sells baby food is interested in the baby food preferences of all families with toddlers from a certain city. A representative from the company sets up a booth at one grocery store in the city that will be used to investigate baby food preference. The representative will ask people with toddlers who walk past the booth to complete the survey. Which of the following best describes the sampling method the company will use?

Convenience sampling

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.

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 compact disc (CD) manufacturer wanted to determine which of two different cover designs for a newly released CD will generate more sales. The manufacturer chose 70 stores to sell the CD. Thirty-five of these stores were randomly assigned to sell CDs with one of the cover designs and the other 35 were assigned to sell the CDs with the other cover design. The manufacturer recorded the number of CDs sold at each of the stores and found a significant difference between the mean number of CDs sold for the two cover designs. Which of the following gives the conclusion that should be made based on the results and provides the best explanation for the conclusion?

It is reasonable to conclude that the difference in sales was caused by the different cover designs because the cover designs were randomly assigned to stores.

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.

Clear-cut harvesting of wood from forests creates long periods of time when certain animals cannot use the forests as habitats. Partial-cut harvesting is increasingly used to lessen the effects of logging on the animals. The following scatterplot shows the relationship between the density of red squirrels, in squirrels per plot, 2 to 4 years after partial-cut harvesting, and the percent of trees that were harvested in each of 11 forests. Which of the following is the best description of the relationship displayed in the scatterplot?

Negative, linear, and strong

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 researcher collected data on the age, in years, and the growth of sea turtles. The following graph is a residual plot of the regression of growth versus age. Does the residual plot support the appropriateness of a linear model?

No, because the graph displays a U-shaped pattern.

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

One-half of the students chose vanilla or chocolate.

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 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 airport, data were recorded for one month on how many baggage items were unloaded from each flight upon arrival as well as the time required to deliver all the baggage items on the flight to the baggage claim area. A scatterplot of the two variables indicated a strong, positive linear association between the variables. Which of the following statements is a correct interpretation of the word "strong" in the description of the association?

The actual time required to deliver all the items to the baggage claim area based on the number of items unloaded will be very close to the time predicted by a least-squares model.

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

For a sample of 42 rabbits, the mean weight is 5 pounds and the standard deviation of weights is 3 pounds. Which of the following is most likely true about the weights for the rabbits in this sample?

The distribution of weights is skewed to the right because the least possible weight is within 2 standard deviations of the mean.

A school is having a contest in which students guess the number of candies in a jar. The student whose guess is closest to the correct number of candies in the jar wins a prize. The number of candies guessed by male and female students is shown in the back-to-back stemplot below. Which of the following statements is true about the distributions of guesses?

The distributions of guesses for male and female students are both skewed to the left.

In a certain computer card game, the player is awarded 5 points for each card that is moved to a correct position. The player is penalized 10 points for each minute the game is played. Let the random variable X represent the number of cards moved to a correct position, and let the random variable Y represent the number of minutes the game is played. The means and standard deviations of the random variables for a particular player are shown in the table below. Assume that X and Y are independent. What are the expected value and the standard deviation of the points per game for the player?

The expected value is -6.5, and the standard deviation is 65.4.

An agricultural scientist wanted to compare the effect of a new fertilizer to that of three older fertilizers—X, Y, and Z—on the growth of vegetables typically grown in small gardens. Two hundred green bean seedlings were individually planted in identical pots and randomly assigned to one of four groups of 50 each. Seedlings in one group were given the new fertilizer, and the three remaining groups of seedlings were given fertilizers X, Y, or Z, respectively. At the end of four weeks, all seedlings were dried and weighed. The scientist found that the mean weight of the seedlings in the group given the new fertilizer was significantly greater than the mean weights of seedlings in the other three groups. The scientist concluded that the new fertilizer was more effective than the other fertilizers for all vegetables. Why is the scientist's conclusion not appropriate?

The experiment only included green beans, so the results cannot be generalized to all vegetables.

An agriculturalist working with Australian pine trees wanted to investigate the relationship between the age and the height of the Australian pine. A random sample of Australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. Based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the Australian pine based on the age, in years, of the tree. predicted height = 0.29 + 0.48(age) Which of the following is the best interpretation of the slope of the regression line?

The height increases, on average, by 0.48 meter each year.

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.

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 child psychologist asked 100 five year olds and 50 ten year olds to name their favorite color. Their results are shown in the following table. Which of the following statements is supported by the table?

The percentage of five year olds who selected red or blue as their favorite color is greater than the percentage of ten year olds who selected red or blue as their favorite color.

The height and age of each child in a random sample of children was recorded. The value of the correlation coefficient between height and age for the children in the sample was 0.8. Based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?

The proportion of the variation in height that is explained by a regression on age is 0.64.

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.

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 sample of 15 golfers who played a golf course on a certain day was selected. For each golfer, the average driving distance (x), in yards, and the percent of fairways hit on the drive (y) were recorded. The scatterplot displays the percent of fairways hit versus the average driving distance. Also shown is the least-squares regression line, y^=66.228+0.0002x. The point circled on the scatterplot is considered an influential point. A new least-squares regression line will be calculated with the influential point removed. How will the removal of the influential point affect the new least-squares regression line for the remaining 14 points?

The y-intercept will increase, and the slope will be negative.

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 roadrunner is a desert bird that tends to run instead of fly. While running, the roadrunner uses its tail as a balance. A sample of 10 roadrunners was taken, and the birds' total length, in centimeters (cm), and tail length, in cm, were recorded. The output shown in the table is from a least-squares regression to predict tail length given total length. Suppose a roadrunner has a total length of 59.0 cm and tail length of 31.1 cm. Based on the residual, does the regression model overestimate or underestimate the tail length of the roadrunner?

Underestimate, because the residual is positive.

As a promotion, the first 50 customers who entered a certain store at a mall were asked to choose from one of two discounts. The first discount choice was 20% off all purchases made that day. The second discount choice was 10% off all purchases for the week. Of those who received the discounts, 28 chose the first discount and 22 chose the second discount. One customer will be selected at random from those who received a discount. Let F represent the event that the selected person chose the first discount, and let S represent the event that the selected person chose the second discount. Are F and S mutually exclusive events?

Yes, because P(F ∩ S)=0.

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