Practice Test 98 - AP Statistics

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. A student observes 20 cars passing an intersection and records whether each car runs a red light. A success is "runs red light," and exactly 20 cars are observed during the same signal cycle length. Does this meet binomial conditions?
2. A school district wants to know whether the proportion of students who prefer block scheduling differs between two grade levels. A random sample of 120 ninth-graders and 150 twelfth-graders was surveyed. Among ninth-graders, 54 preferred block scheduling; among twelfth-graders, 93 preferred block scheduling. Which inference procedure is most appropriate to answer the research question?
3. A bookstore tracks the number of books purchased in a single transaction by a randomly selected customer. Let $X$ be the number of books, a discrete random variable with $\mu_X=1.8$ books and $\sigma_X=1.3$ books. Which interpretation of the standard deviation is correct?
4. A random sample of 80 packaged salads from a factory found that 12 were underweight. A 99% confidence interval for the true proportion $p$ of all packaged salads from that factory that are underweight is $(0.06,\ 0.24)$. Which interpretation is correct?
5. A dataset of the last digit of 1,000 telephone numbers is collected. Which of the following best describes the likely shape of the distribution of these digits?
6. A number is selected at random from the integers $1$ through $20$, inclusive. Define event $A$ as "the number is even" and event $B$ as "the number is a multiple of 5." Are the two events mutually exclusive?
7. A nonprofit claims that 50% of donors prefer to be contacted by email rather than phone. A random sample of 100 donors finds that 61 prefer email. A one-sample proportion test is performed at $\alpha=0.05$ with hypotheses $H_0:p=0.50$ and $H_a:p\ne0.50$. The test yields a $p$-value of 0.04, so the decision is to reject $H_0$. Which conclusion is appropriate?
8. A museum studies whether visitor age group is associated with preferred exhibit type. A random sample of visitors is surveyed and classified by age group (Child, Adult, Senior) and preferred exhibit (Art, History, Science). The results are shown below. A chi-square test of independence is performed and results in $p=0.030$. What conclusion is appropriate at the $\alpha=0.05$ level? Two-way table (counts):

   Age group	Art	History	Science
   Child	20	15	45
   Adult	55	60	35
   Senior	40	55	15

9. A teacher wants to know whether participation in an optional review session is related to exam outcome. From a single random sample of 180 students enrolled in a course, the teacher records whether each student attended the review session (Yes/No) and whether they passed the exam (Pass/Fail). The results are shown in the two-way table. Which chi-square test is appropriate, and what are the correct hypotheses? Note: One sample; two categorical variables.
10. A marine biologist studies whether ocean depth in meters ($x$) predicts water temperature in °C ($y$) at sampling locations. The biologist expects that greater depth corresponds to lower temperature in the population. Which hypotheses are appropriate for testing this expectation about the slope in the regression of $y$ on $x$?
11. In a survey of 200 students, 90 reported that they play a sport (S), 120 reported that they have a part-time job (J), and 50 reported both playing a sport and having a part-time job. One student is selected at random. Let Event A be "the student plays a sport" and Event B be "the student has a part-time job." Which statement about Events A and B is correct?​
12. A school district studies the height (in inches) of individual 10th-grade students. The population mean is $\mu=66$ inches and the population standard deviation is $\sigma=3.5$ inches. A researcher repeatedly selects simple random samples of size $n=100$ and computes the sample mean height $\bar{x}$. Which statement about the sampling distribution of $\bar{x}$ is correct?
13. A school district completed a study to evaluate whether a new online homework platform improves Algebra I quiz scores. From all 12 high schools in the district, administrators randomly selected 240 Algebra I students (20 per school). Within each school, the selected students were randomly assigned to either use the new platform for 6 weeks or continue with the usual homework system. At the end of 6 weeks, all selected students took the same district quiz, and the platform group had a higher average score. Which conclusion is justified based on the design of this study?
14. A sports scientist examines whether the number of hours of sleep the night before a race ($x$) predicts a runner's 5K time ($y$, in minutes). Using data from 35 runners, a least-squares regression of time on sleep is fit. The scientist's claim is that more sleep leads to faster times (smaller minutes), implying a negative population slope. Which hypotheses are appropriate for testing the population regression slope consistent with this claim?
15. A researcher tests whether a new fertilizer changes the mean height of a certain plant. They test $H_0: \mu=18$ cm vs. $H_a: \mu\neq18$ cm at $\alpha=0.05$. The p-value is 0.64, so they fail to reject $H_0$. In reality, the true mean height with the fertilizer is $\mu=18$ cm. Which type of error was made?
16. A streaming service reports that the proportion of subscribers who use the family plan is $0.30$. A consumer group wonders if the true proportion is different. In a random sample of $n=500$ subscribers, $170$ use the family plan (sample proportion $\hat{p}=0.340$). Which hypotheses are appropriate?
17. A student investigates whether hours of sleep ($x$) predicts quiz score ($y$) for 30 classmates and fits the least-squares regression line. A slope test is performed with hypotheses $H_0: \beta_1=0$ versus $H_a: \beta_1\neq 0$. The computer output reports a two-sided p-value of 0.018 for the slope. Using a 0.05 significance level, the student decides to reject $H_0$. Based on this completed slope test, what conclusion is appropriate?
18. A city wants to estimate the mean number of minutes all residents spend commuting to work each day. A researcher stands at a downtown bus terminal from 7:00–8:00 a.m. on Tuesday and randomly selects every 10th person who enters to answer a commuting-time question. Which issue most threatens the validity of generalizing the results to all residents?
19. A school district wants to know whether a new online homework platform changes the mean weekly math homework time for 9th graders. Researchers randomly sample 80 students from the district and randomly assign 40 to use the new platform and 40 to use the old platform for 6 weeks. At the end, each student reports total minutes spent on math homework in a typical week. Which inference procedure is most appropriate to assess whether the mean weekly homework time differs between platforms?
20. A state agency wants to estimate the mean number of hours per week that all adults in the state exercise. They use a list of landline phone numbers and call a simple random sample of 1,500 numbers from that list. Which issue most threatens the validity of generalizing to all adults in the state?

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