Practice Test 92 - AP Statistics

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

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1. A streaming service records the number of episodes watched in one sitting by 65 users on a particular day, counted automatically by the app (whole episodes). The dotplot shows the distribution. Dotplot of episodes watched 1 | ••••••••••••••••••••• 2 | ••••••••••••• 3 | •••••••• 4 | ••••• 5 | ••• 6 | •• 7 | • 8 | • Which feature is most evident?
2. An environmental scientist tests whether distance from a highway is associated with noise level. She selects 25 measurement sites (observational units) and records the distance from the highway in meters and the average sound level in decibels (dB) during a 5-minute interval. The goal is to see whether noise decreases as distance increases. Which classification is correct?
3. A researcher compares mean weekly study time (in hours) for students using a new study app versus a traditional planner. From independent random samples, a 95% confidence interval for the population mean difference $(\mu_{\text{app}}-\mu_{\text{planner}})$ is $(1.2,\ 4.8)$. Which interpretation is correct?
4. A school counselor collects data from 28 students on $x$ = number of hours of sleep on a school night and $y$ = score on a memory quiz (out of 50). A least-squares regression of quiz score on sleep produces a 95% confidence interval for the population slope $\beta$ of $(1.2,\ 3.8)$. Which interpretation is correct?
5. A tech company tests whether a new interface reduces average customer support time. They use $H_0: \mu=12$ minutes vs. $H_a: \mu<12$ minutes at $\alpha=0.05$. They reject $H_0$ and announce the interface reduced mean support time. In reality, the true mean support time with the new interface is still $\mu=12$ minutes. Which type of error was made?
6. A casino observes 50 spins of a roulette wheel and records whether the ball lands on red. A success is "red," and exactly 50 spins are observed. Assume the wheel is fair and each spin is independent. Does this meet binomial conditions?
7. A random sample of 1,000 adults in a state found that 610 approve of the governor's job performance. A 95% confidence interval for the true proportion $p$ of all adults in the state who approve is $(0.58,\ 0.64)$. Which interpretation is correct?
8. A cell has expected count 30, row total 120, table total 400. Its column total is?
9. A bar chart shows the number of home runs hit by four baseball players in a season: Alvarez (42), Benson (35), Cruz (35), and Diaz (28). Which of the following statements is a correct interpretation of the chart?
10. A manufacturer claims the population mean lifetime of its batteries is $\mu=12$ hours. A random sample of batteries is tested and a 95% confidence interval for $\mu$ is found to be $(11.3,\ 11.9)$. Is the claim supported by the CI?
11. A tech company tests whether a new website layout increases the proportion of visitors who make a purchase above the current rate of 0.12. The hypotheses are $H_0: p=0.12$ versus $H_a: p>0.12$, with $\alpha=0.05$. The p-value from the test is 0.001. Which interpretation of the p-value is correct?
12. A nutritionist compares mean daily sodium intake (mg) for two groups: adults who cook at home and adults who primarily eat out. She takes an independent random sample of $n_H=25$ from the home-cooking group and $n_E=25$ from the eat-out group. Consider the sampling distribution of $\bar{x}_H-\bar{x}_E$. Which statement is correct?
13. A school nurse wants to test whether a new mindfulness app reduces students' stress. She recruits 60 volunteers from one high school and measures each student's stress score (0–50 scale) after 2 weeks. Students' names are put in a hat and 30 are randomly assigned to use the mindfulness app daily; the other 30 are assigned to continue their usual routine. The nurse compares the mean stress scores between groups. Which feature of this design allows a cause-and-effect conclusion about the app's impact on stress?
14. A teacher records the number of text messages students send in a day. The population distribution is right-skewed because a few students send extremely many messages. She takes many random samples of $n=30$ students and computes the sample mean texts per day $\bar{x}$, then looks at the sampling distribution of $\bar{x}$. Why is the sampling distribution approximately normal?
15. An online course historically has a 60% completion rate. In a new cohort of 15 independently enrolled students, the instructor expects about 9 completions but observes 3 completions. Assuming the 60% rate still applies, is this result unexpected given the variability in a group of 15?
16. An online retailer tested whether a new checkout design changes the proportion of visitors who complete a purchase. Visitors were randomly assigned to the old design (Design O) or the new design (Design N). In the experiment, 78 of 600 visitors using Design O purchased, and 95 of 620 visitors using Design N purchased. A two-proportion $z$ test at $\alpha=0.01$ tested $H_0: p_O=p_N$ versus $H_a: p_O\ne p_N$, where $p_O$ and $p_N$ are the true purchase proportions under each design. The p-value was 0.008. What conclusion is appropriate?
17. A bookstore owner claims that between 35% and 45% of customers buy a magazine at checkout. A random sample of customers is observed, and a 95% confidence interval for the true proportion $p$ is $(0.37,\ 0.44)$. Is the claim supported by the confidence interval?
18. An environmental scientist recorded daily rainfall (in mm) on 90 days during a season. The summaries were: mean = 6.8 mm, median = 2.1 mm, SD = 12.4 mm, five-number summary = (min 0.0, $Q_1$ 0.0, median 2.1, $Q_3$ 7.0, max 85.0), and IQR = 7.0 mm. Which interpretation is correct?
19. A call center monitors 12 incoming calls and records whether each caller is satisfied with the help received. Based on historical data, the probability a caller is satisfied is $0.68$, and calls are treated as independent. Let $X$ be the number of satisfied callers among the 12. Which values correctly model this situation with a binomial distribution (identify $n$ and $p$)?
20. A fitness center recorded whether members attend morning classes or evening classes and whether they renewed their membership. The two categorical variables are Class time (Morning/Evening) and Renewal (Renewed/Did not renew). Using the two-way table, which comparison is appropriate for assessing whether class time is associated with renewal? Which comparison is appropriate?

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