Maybe AP Stats Test Unit 8&9

Eastwood 2025

A food scientist conducting a study to investigate the nutritional habits of teenagers in a city selected a random sample of 100 teenagers in the city. Each of the 100 teenagers was asked to complete a survey with questions about age and the number of ounces of carbonated drinks consumed on the previous day.
Assuming the conditions for inference have been met, which of the following is an appropriate test and alternative hypothesis to use to investigate whether the average number of ounces of carbonated drinks consumed in a day increases with age for teenagers in the city?
Responses
A
A 𝑡-test for the slope of a regression model with alternative hypothesis: Ha:𝛽>0
B
A 𝑡-test for the slope of a regression model with alternative hypothesis: Ha:𝛽<0
C
A 𝑡-test for the slope of a regression model with alternative hypothesis: Ha:𝛽=0
D
A one-sample 𝑧-test for a population proportion with alternative hypothesis: Ha:𝑝>0.5

A 𝑡-test for the slope of a regression model with alternative hypothesis: Ha:𝛽>0

A veterinarian keeps track of the types of animals treated by an animal clinic. The following distribution represents the percentages of animals the clinic has historically encountered.

If the animal clinic treats 230 animals in a month, how many of each animal type would be expected?

:)

A polling organization uses random digit dialing of registered voters in a county to gauge the voters’ opinions about a ballot initiative to increase taxes for a new county park. The organization will investigate whether there are differences in responses based on the highest level of education completed. The phone survey asked voters whether they approve or disapprove of the tax increase and their highest level of education completed: high school, bachelor’s degree, or master’s degree.

Which of the following is the appropriate test to investigate whether there is an association between opinion about the ballot initiative and the highest level of education completed?

A. A two-sample t-test for a difference between means
B. A two-sample z-test for a difference between proportions
C. A chi-square test of homogeneity
D. A chi-square test of independence

D. A chi-square test of independence

Ecologists conducted a study to investigate the potential ecological impact of golf courses. Investigators monitored the reproductive success of bluebirds in birdhouses at nine golf courses and ten similar birdhouses at nongolf sites. Data on nests in birdhouses occupied only by bluebirds are shown in the table.

Observed Number of Nests per Birdhouse by Location	0 nests	1 nest	2 or 3 nests	Total
Golf	30	42	8	80
Nongolf	40	58	22	120
Total	70	100	30	200

If the proportions of nests occupied are the same for golf and nongolf sites, what would be the expected count of birdhouses with 1 nest in nongolf locations?

A. 40
B. 42
C. 50
D. 58
E. 60

E. 60

Students in a high school statistics class wanted to see if the distribution of the colors of a popular candy was different in the bags for different types of candies the company manufactures. The students purchased several large bags of regular candies, tropical-flavored candies, and sour-flavored candies. For each type of candy, the students took a random sample of 100 candies and recorded how many of each color (red, green, yellow, or blue) were in the sample. The students verified the conditions for inference and calculated a chi-square test statistic of 12.59 with a corresponding p-value of 0.05. Which of the following is the correct interpretation of the p-value in the context of the test?

A
The hypothesis test has a significance level of α=0.05.
B
There is a 5 percent chance that the distribution of colors is different for the different types of candies.
C
There is a 5 percent chance that the distribution of colors is the same for the different types of candies.
D
Assuming that the distribution of colors for the different types of candies is the same, there is a 5 percent chance of finding a test statistic of 12.59 or larger.
E
Assuming that the distribution of colors for the different types of candies is different, there is a 5 percent chance of finding a test statistic of 12.59 or larger.

D
Assuming that the distribution of colors for the different types of candies is the same, there is a 5 percent chance of finding a test statistic of 12.59 or larger.

A survey of a random sample of 210 male teens and 228 female teens, ages 13 years to 17 years, found that 122 of the male teens and 160 of the female teens brush their teeth at least twice a day. If there is no difference between the proportions in the population of all male and female teens ages 13 years to 17 years who brush their teeth at least twice a day, approximately how many males and females in the sample would be expected to brush their teeth at least twice a day?

(A) 105 males and 114 females

(B) 122 males and 160 females

(C) 135 males and 147 females

(D) 141 males and 141 females

(E) 219 males and 219 females

C. 135 males and 147 females

A fisheries biologist collected a random sample of fish from a lake and conducted a chi-square goodness-of-fit test to see if the distribution of fish changed over time. The table below shows the distribution of fish that were put into the lake when it was originally stocked. The biologist found evidence to reject the null hypothesis in favor of the alternative hypothesis. Which of the following represents the alternative hypothesis of the test?

A. At least one of the fish proportions is different than the corresponding proportion when the lake was originally stocked

B. The proportions for the different fish types are the same as the corresponding proportions when the lake was originally stocked.

C. The proportions are evenly distributed among fish types.

D. At least one of the fish proportions is the same as the corresponding proportion when the lake was stocked.

E. All of the fish proportions are different than the corresponding proportions when the lake was stocked.

A. At least one of the fish proportions is different than the corresponding proportion when the lake was originally stocked

An administrator at a local high school wants to investigate whether there is an association between the grade level of a student (either ninth, tenth, eleventh, or twelfth) and how the student commutes to school (either walks, bikes, takes the bus, receives a ride, or drives). After a chi-square test for association was conducted, the results indicated that the chi-square test statistic was 14.63 with a p-value of 0.2623.

Which of the following is the correct interpretation of the p-value in the context of the test?

a. There is a 26.23 percent chance that grade level and how a student commutes to school are independent.

b. There is a 26.23 percent chance that there is no association between grade level and how a student commutes to school.

c. Assuming there is no association between a student's grade level and how the student commutes to school, there is a 26.23 percent chance of finding a test statistic that is 14.63 or larger.

d. Assuming that a student's grade level and the way the student commutes to school are dependent, there is a 26.23 percent chance of finding a test statistic that is 14.63 or larger.

e. Assuming that a student's grade level and the way the student commutes to school are dependent, there is a 26.23 percent chance of finding a test statistic that is 14.63 or smaller.

c. Assuming there is no association between a student's grade level and how the student commutes to school, there is a 26.23 percent chance of finding a test statistic that is 14.63 or larger.

A reporter intends to survey residents of a city to investigate whether there are differences in the use of grocery delivery services by the region of the city where the residents live (north, south, west, and east). City residents will be asked to respond yes or no to the question, “Do you regularly use a grocery delivery service to purchase groceries?” Results will be collected in a 4-by-2 table of counts organized by region and response to the question.

For a chi-square test for homogeneity, which of the conditions listed below is not necessary to investigate whether there are differences between the use of grocery delivery service by region?

A. For each cell in the table, (row total)(column total)/table total will be greater than 5.

B. Data should be collected using a stratified random sample, with region as strata.

C. All eight expected cell counts should be greater than 5.

D. The number of residents sampled from each region should be greater than 30.

E. The total number of residents sampled should be at most 10 percent of the total number of residents in the city.

D. The number of residents sampled from each region should be greater than 30.

For which of the following is a chi-square goodness-of-fit test most appropriate?
A
Estimating a difference between two population means
B
Estimating a difference between two population proportions
C
Finding the expected value of a probability distribution
D
Determining whether a categorical variable has a significantly different distribution of proportions than the expected distribution
E
Determining the best shape for a set of data

D
Determining whether a categorical variable has a significantly different distribution of proportions than the expected distribution

Nonnative speakers of English often have characteristics in their handwriting that differ depending on the speaker's first language. Handwriting samples from a random sample of Chinese, Malay, and Indian children in a school in Singapore were taken to investigate these differences. One characteristic of interest was a rounding at the top of the capital letter A. Data for the top-rounding characteristic for a sample of 153 children are shown in the table below:

	Malay	Indian	Chinese	Total
Yes	9	21	8	38
No	42	31	42	115
Total	51	52	50	153

If children from these countries exhibit top rounding in the same proportions, what is the expected count for Malay children who show top rounding?

A) 9/38
B. 9/51

C. 9

D. ((38)(51)/153)

E. ((38)(9)/153)

D. ((38)(51)/153)

A chi-square goodness-of-fit test, where all assumptions were met, yielded the test statistic x2=12.4. Henry claims the corresponding p-value of 0.03 means that the probability of observing a test statistic of x2=12.4 is 0.03, assuming the null hypothesis is true.

Which of the following is a valid criticism of this interpretation of the p-value?

A. The null hypothesis can never be assumed to be true.

B. The null hypothesis is not stated.

C. The p-value is not the probability of observing 12.4 exactly.

D. The significance level is not stated.

E. The degrees of freedom are not stated.

C. The p-value is not the probability of observing 12.4 exactly.

In order to plan its next advertising campaign, the Trendy Motor Vehicle Company is investigating whether the type of vehicle and the color of the vehicle are related. Each person in a random sample of size 275, selected from the company's mailing list, was classified according to the type (car or truck) and the color of vehicle he or she drove. The data are shown in the table below.

Which of the following procedures would be most appropriate to use for investigating whether there is a relationship between vehicle type and color?

A
A two-sample t-test

B
A two-sample z-test

C
A matched pairs t-test

D
A chi-square goodness-of-fit test

E
A chi-square test of independence

E
A chi-square test of independence

A company claims it audits its employees' transactions based on their job level. For entry-level positions, the company claims that 50 percent get a basic audit, 30 percent get an enhanced audit, and 20 percent get a complete audit. The company tests this hypothesis using a random sample and finds χ 2=0.771 with a corresponding p-value of 0.68. Assuming conditions for inference were met, which of the following is the correct interpretation of the p-value?

A. There is a 68 percent chance of obtaining a chi-square value of at least 0.771.

B. There is a 68 percent chance that the company's claim is correct.

C. If the null hypothesis were true, there would be a 68 percent chance that the company's claim is correct.

D. If the null hypothesis were true, there would be a 68 percent chance of obtaining a chi-square value of at least 0.771.

D. If the null hypothesis were true, there would be a 68 percent chance of obtaining a chi-square value of 0.771.

A sports physician conducted a study to investigate whether there is an association between running experience and the occurrence of a certain sport injury for marathon runners while training for a marathon. Data were collected on a random sample of 51 marathon runners. Each runner from the sample was categorized by running experience (low, medium, high) and whether or not the runner experienced the sport injury while training for a marathon. The conditions for inference were met, and a χ² test statistic of approximately 8.12 was calculated.

Which of the following describes the p-value of the test?

A.p-value > 0.25

B. 0.10 <p-value < 0.25

C. 0.05 <p-value < 0.10

D. 0.01 <p-value < 0.05

E.p-value < 0.01

D. 0.01 <p-value < 0.05

Which of the following is a reason not to use a chi-square test of homogeneity to analyze a set of data?

A. The data consist of one categorical variable for two or more different populations and are summarized by counts in a two-way table.

B. The data were obtained through a simple random sample from a single population and summarized by counts on two categorical variables.

C. The data were obtained from more than two populations to investigate whether the proportions for categorical data collected are the same.

D. The data were obtained from four different regions to investigate whether the distribution of a categorical variable is different across the four regions.

E. The data were obtained using a simple random sample of a population from last year and a simple random sample of the same population from this year where the data collected were categorical variables.

B. The data were obtained through a simple random sample from a single population and summarized by counts on two categorical variables.

pic

III only

A scientist is investigating whether percent concentration can be used to predict density in apple juice. A scientist selected a random sample of 12 apple juice varieties and recorded the density, in pounds per cubic inch, and the percent concentration of each apple juice variety. The scientist wants to estimate the mean change in the density, in pounds per cubic inch, for each increase of 1 percent concentration of apple juice. Assuming the conditions for inference have been met, which of the following inference procedures is most appropriate for this investigation?

a. A linear regression t-interval for slope.

b. A matched-pairs t-interval for a mean difference.

c. A two-sample t-interval for a difference between means.

d. A one-sample t-test for means.

e. A two-sample z-interval for a difference between proportions.

a. A linear regression t-interval for slope

Researchers are examining the relationship between hours of sleep and athletic performance among college athletes. Athletic performance will be measured on a numeric scale, with greater numbers indicating better performance. The researchers expect that the more hours the athletes sleep, the better they will perform. Assuming all conditions for inference are met, the researchers will create a 95 percent confidence interval for the slope of the regression line for predicting athletic performance from the amount of sleep.

For which of the following would the confidence interval support the researchers' expectations?

A. The confidence interval includes only positive values.

B. The confidence interval includes only negative values.

C. The confidence interval has a width less than 1.

D. The confidence interval has a width greater than 1.

E. The confidence interval includes the value 0.

A. The confidence interval includes only positive values.

A baseball enthusiast carried out a simple linear regression to investigate whether there is a linear relationship between the number of runs scored by a player and the number of times the player was intentionally walked. Computer output from the regression analysis is shown.

Let β represent the slope of the population regression line used to predict the number of runs scored from the number of intentional walks in the population of baseball players. A t-test for a slope of a regression line was conducted for the following hypotheses.

H0:β=0

Ha:β≠0

What is the appropriate test statistic for the test?

t = 16/2.073

t = 16/0.037

t = 0.50/0.037

t = 0.50/2.073

t = 0.50/0.63

t = 0.50/0.037

The number of shots taken and points scored by 8 players in a basketball game are shown in the table.

Number of shots taken 1 4 7 8 10 11 11 14

Number of points scored 0 4 8 9 14 12 15 22

A basketball coach is investigating whether the number of shots taken can be used to predict the mean number of points scored. Assuming the conditions for inference have been met, which of the following inference procedures is the most appropriate to estimate the mean change in the number of points scored for each increase of 1 shot taken?

A. A one-sample t-interval for means.

B. A linear regression t-interval for slope.

C. A two-sample t-interval for a difference between means.

D. A matched-pairs t-interval for a mean difference.

E. A two-sample z-interval for a difference between proportions.

B. A linear regression t-interval for slope.

A zoologist selected 12 black bears in a Canadian habitat at random to examine the relationship between the age in years, x, and the weight in tens of pounds, y. The 95 percent confidence interval for estimating the population slope of the linear regression line predicting weight in tens of pounds based on the age in years is given by 1.272±0.570. Assume that the conditions for inference for the slope of the regression equation are met.

Which of the following is the correct interpretation of the interval?

A. We are 95 percent confident that the mean increase in the weight of a black bear for each one-year increase in the age of the bear is between 7.0 and 18.4 pounds.

B. We are 95 percent confident that an increase of one year in the age of an individual black bear will result in an increase in the black bear's weight of between 7.0 and 18.4 pounds.

C. We are 95 percent confident that for every one-year increase in the age of black bears in the sample, the average increase in the weights of those black bears is between 7.0 and 18.4 pounds.

D. We are 95 percent confident that the mean increase in the age of a black bear for each one-pound increase in the weight of the black bear is between 7.0 and 18.4 years.

E. We are 95 percent confident that any sample of 12 black bears will produce a slope of the regression line between 7.0 and 18.4.

A

A car retailer wanted to see if there is a linear relationship between overall mileage and the suggested retail price of a car. The retailer collected data on 18 cars of a similar type selected at random and used the data to test the claim that there is a linear relationship. The following hypotheses were used to test the claim:

H0: β = 0

Ha: β ≠ 0

The test yielded a t-value of 2.186 with a corresponding p-value of 0.044. Which of the following is the correct interpretation of the p-value?

A) If there is a linear relationship between overall mileage and the suggested retail price of a car, the probability of observing a test statistic at least as extreme as 2.186 is 0.044.

B) If there is not a linear relationship between overall mileage and the suggested retail price of a car, the probability of observing a test statistic at least as extreme as 2.186 is 0.044.

C) If there is not a linear relationship between overall mileage and the suggested retail price of a car, the probability of observing a test statistic of 2.186 or greater is 0.044.

D) If there is not a linear relationship between overall mileage and the suggested retail price of a car, the probability of observing a test statistic of 2.186 is 0.044.

E) If there is a linear relationship between overall mileage and the suggested retail price of a car, the probability of observing a test statistic of 2.186 or greater is 0.044.

B) If there is not a linear relationship between overall mileage and the suggested retail price of a car, the probability of observing a test statistic at least as extreme as 2.186 is 0.044.

A seafood festival organizer is interested in whether there is a relationship between the number of ingredients in the clam chowders entered in the festival’s clam chowder contest and the ratings given to the chowders by the judges. The organizer requires each of the twelve restaurants in the competition to list all of its chowder's ingredients and requires each judge who tastes the clam chowders to rate each chowder from one through ten on a note card. The organizer then randomly selects twenty-five note cards. Assuming that all conditions for inference are met, which of the following significance tests should be used to investigate whether having more ingredients in the chowders is associated with a reduction in the ratings given to the chowders by the judges?

A) A chi-square test of independence
B) A two-sample t-test for a difference between means
C) A two-sample z-test for a difference between proportions
D) A linear regression t-test for slope
E) A matched pairs t-test for a mean difference

D) A linear regression t-test for slope

pic

The variance of the response variable is constant for all values of the explanatory variable.

To investigate the relationship between the selling price of a house, y, in dollars, and the size of the house, x, in square feet, a local builder collected data on a random sample of 120 houses from a certain region. Assume that the conditions for inference for the slope of a regression line are met. The resulting 95 percent confidence interval for the population slope of the regression line relating price and size is given by (62, 99).

The local builder claims that the selling price of houses from the region increases by $104 for every extra square foot of space in the house. Which of the following best describes the conclusion that can be reached about this claim based on the confidence interval?

A. The claim is supported by the interval, since the interval does not contain the value 0.

B. The claim is supported by the interval, since all values in the interval are positive.

C. The claim is supported by the interval, since the interval does not contain the value 104.

D. The claim is not supported by the interval, since the interval does not contain the value 0.

E. The claim is not supported by the interval, since the interval does not contain the value 104.

E. The claim is not supported by the interval, since the interval does not contain the value 104.

pic

0.583 plus or minus (2.080)(0.138)

A scientist claims that there is a linear relationship between a lake's flow rate and its runoff factor. The scientist collected data and tested this claim at a significance level of α=0.05. The following hypotheses were tested:

Null hypothesis (Ho):β=0

Alternative hypothesis (Ha):βnot=0

The scientist found a p-value of 0.02 for the test. Which of the following is a correct conclusion about the scientist's claim?

a) The null hypothesis is rejected since 0.02 < 0.05. There is sufficient statistical evidence to suggest that there is a linear relationship between a lake's flow rate and runoff factor.

b) The null hypothesis is not rejected since 0.02 < 0.05. There is sufficient evidence to suggest that there is a linear relationship between a lake's flow rate and runoff factor.

c) The null hypothesis is rejected since 0.02 < 0.05. There is not sufficient evidence to suggest that there is a linear relationship between a lake's flow rate and runoff factor.

d) The null hypothesis is accepted since 0.02 < 0.05. There is sufficient evidence to suggest that there is not a linear relationship between a lake's flow rate and runoff factor.

a) The null hypothesis is rejected since 0.02 < 0.05. There is sufficient statistical evidence to suggest that there is a linear relationship between a lake's flow rate and runoff factor.