Practice Test 100 - AP Statistics

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

A librarian recorded the number of books checked out by each of 55 patrons on a Saturday, using the library's checkout system. The dotplot below shows the distribution. Dotplot (books checked out): 0 | •••••••••••••••• 1 | ••••••••••• 2 | ••••••• 3 | •••• 4 | ••• 5 | •• 6 | • 7 | • 8 | 9 | 10| • Which feature of the distribution is most evident?
A school district investigates the research question: "Do students who attend after-school tutoring score higher on the end-of-course math exam than students who do not?" The population is all students in the district taking the exam. Counselors invite students who are struggling in math to attend tutoring; at the end of the term, the average exam score for tutoring attendees is 68, while non-attendees average 74. The district concludes that attending tutoring lowers math exam scores. Which statement explains whether the conclusion is valid?
A smartphone manufacturer states that the mean time to fully charge its new phone model is 80 minutes. A reviewer randomly tests $n=15$ phones and finds a sample mean charge time of $\bar{x}=84$ minutes. The reviewer wants to test whether the true mean charge time is greater than 80 minutes. Which hypotheses are appropriate?
A student repeatedly spins a fair spinner with 4 equal sections labeled A, B, C, and D. The first 24 spins are recorded in order as: A, B, A, C, A, D, A, B, A, C, A, D, A, B, A, C, A, D, A, B, A, C, A, D. The student claims the spinner is "not random" because the results repeat a clear 6-spin cycle. Is the pattern consistent with random behavior?
A spinner is divided into 8 equal sections labeled 1 through 8, and it is spun once. Let event $A$ be "the result is a multiple of 3" and event $B$ be "the result is greater than 6." The outcome 6 is a multiple of 3 but is not greater than 6, while outcomes 7 and 8 are greater than 6 but not multiples of 3. No outcome satisfies both conditions. Are the two events mutually exclusive?
A teacher has a bag of 500 candies, 100 of which are sour. The teacher randomly selects 25 candies without replacement and records whether each is sour. A success is "sour," and exactly 25 candies are selected. Does this meet binomial conditions?
A cafeteria manager believes that more than 25% of students choose the vegetarian option on Fridays. In a random sample of 160 students eating lunch on a Friday, 49 chose the vegetarian option. A one-proportion $z$ test was performed for $H_0: p=0.25$ versus $H_a: p>0.25$ at $\alpha=0.05$ . The $p$ -value was 0.11, so the manager failed to reject $H_0$ . Which conclusion is appropriate?
A school compares the mean number of hours of sleep per night for students who participate in a sport versus those who do not. The claim is that athletes sleep more on average. A 95% confidence interval for the difference in means, defined as $\mu_{\text{athletes}} - \mu_{\text{nonathletes}}$ , is $(0.3, 1.1)$ hours. Is the claim supported by the confidence interval?
A news organization takes a simple random sample of 1,200 adults nationwide and asks whether they approve of a public official's job performance. In the sample, 624 approve. A 95% confidence interval for the true proportion $p$ of all adults nationwide who approve is $(0.49,\ 0.55)$ . Which interpretation is correct?
A manufacturer tests a random sample of airbags from a production run and uses a hypothesis test to decide whether the defect rate exceeds the safety threshold. The test result leads the company to either recall the run or ship it. Why is it important to consider potential error when interpreting the test result, given the cost of a recall and the risk of injuries if defective airbags are shipped?
A biology teacher wants to test whether a new review activity improves quiz scores compared with the usual review. There are six class periods, and students in different periods tend to have different average performance because of scheduling and course load. The teacher can implement only one review method per class period to avoid students sharing materials across groups. Which experimental design is most appropriate given this constraint?
A fitness app claims the mean number of steps users take per day is $\mu=10{,}000$ . From a random sample of users, a 95% confidence interval for $\mu$ is $(9{,}450,\,9{,}980)$ . Is the claim supported by the confidence interval?
A researcher compares mean reaction time (in milliseconds) between people who drank caffeinated coffee and people who drank decaf. A random sample of $n=44$ caffeinated participants had mean $\bar{x}=241$ ms, and a random sample of $n=46$ decaf participants had mean $\bar{x}=255$ ms. The research claim is that caffeine decreases the population mean reaction time. Which hypotheses are appropriate?
A credit union studies the dollar amount of ATM withdrawals. The population distribution is right-skewed because most withdrawals are small, with a few very large withdrawals. The analyst repeatedly takes random samples of $n=35$ withdrawals and computes the sample mean withdrawal amount $\bar{x}$ . She looks at the sampling distribution of $\bar{x}$ . Why is the sampling distribution approximately normal?
A school district wants to estimate the proportion of all high school students in the district who get at least 8 hours of sleep on school nights. A student researcher stands in the cafeteria of one high school for two days and asks every student who walks by between 11:30 a.m. and 12:00 p.m. to complete a quick survey; 312 students respond. Which statement best describes the sample representativeness?
A runner logs times. Let $X$ be the time (in minutes) for the first half of a route and $Y$ be the time (in minutes) for the second half. Assume $X$ and $Y$ are independent, with $\mu_X=24$ , $\sigma_X=2.5$ , $\mu_Y=26$ , and $\sigma_Y=3.5$ . Define $R=Y-X$ , the second-half time minus first-half time. Which statement about $R$ is correct?
A political scientist tests whether support for 3 candidates is distributed as 45% for Candidate A, 35% for Candidate B, and 20% for Candidate C. A random sample of 250 likely voters is surveyed, producing the counts shown in a table. A chi-square goodness-of-fit test yields a p-value of 0.088 for testing $H_0$ : the population proportions match 0.45/0.35/0.20 vs. $H_a$ : they do not. What conclusion is appropriate at the $\alpha=0.10$ level?
A fitness trainer records data from 40 clients on $x$ = number of weeks in a training program and $y$ = change in resting heart rate (beats per minute, where negative values indicate a decrease). The regression of change on weeks gives a 90% confidence interval for the population slope $\beta$ of $(-1.5,\ -0.3)$ . Which interpretation is correct?
A coffee shop claims its mean wait time for a drink is less than 4 minutes. A random sample of 40 orders was taken, and a one-sample $t$ test was performed with $H_0: \mu = 4$ minutes and $H_a: \mu < 4$ minutes at significance level $\alpha=0.05$ . The test produced a p-value of 0.03. What conclusion is appropriate?
A university compared the proportion of students who report high stress in two majors. In random samples, 120 of 200 engineering students and 102 of 210 business students reported high stress. A 95% confidence interval for the difference $p_{eng} - p_{bus}$ is $(0.03,\ 0.21)$ . Which interpretation is correct?

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