Practice Test 16 - AP Statistics

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

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1. 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. The district has 4 high schools. A researcher visits the largest high school during lunch on one Friday and surveys 250 students who are sitting in the cafeteria at that time. No random selection method is used; students can decline. Which statement best describes the sample representativeness?
2. A manufacturer compares the mean lifetime (hours) of bulbs from Machine X and Machine Y. Random samples of bulbs were selected from each machine's production. A two-sample $t$ test was performed for $H_0: \mu_X-\mu_Y=0$ versus $H_a: \mu_X-\mu_Y>0$. The p-value was 0.055. Using $\alpha=0.05$, what conclusion is appropriate?
3. A city measured the commute time (in minutes) for 60 randomly selected workers. The summaries were: mean = 31.2, median = 30, SD = 8.5, five-number summary = (min 14, $Q_1$ 25, median 30, $Q_3$ 36, max 49), and IQR = 11. Which interpretation is correct?
4. A school district claims the mean time (in minutes) that high school students spend on homework per week is $\mu=420$. A random sample of students was used to construct a 95% confidence interval for $\mu$ of $(390,\ 450)$. Is the claim supported by the confidence interval?
5. A university expects the distribution of students' primary commute methods to be: 50% Car, 20% Bus, 15% Bike, 10% Walk, 5% Other. A random sample of 300 students reports: Car 141, Bus 72, Bike 39, Walk 33, Other 15. A chi-square goodness-of-fit test of $H_0$: the population distribution matches the expected proportions yields $p$-value = 0.27. Expected counts under $H_0$ are: Car 150, Bus 60, Bike 45, Walk 30, Other 15. What conclusion is appropriate at $\alpha=0.05$?​
6. A public health researcher estimates the proportion $p$ of adults in a city who received a flu vaccine this year. From a random sample of 250 adults, 120 report being vaccinated. A 90% confidence interval for $p$ is $(0.432, 0.528)$. Which interpretation is correct?
7. A teacher compares, for 14 students, number of absences (days) and final exam score (points out of 100). The scatterplot shows a weak downward trend with substantial scatter. Which statement about correlation is correct?
8. A nutritionist tests whether the mean sodium content of a certain canned soup is less than the advertised 700 mg per serving. A random sample of 12 cans is selected, and conditions for a one-sample $t$ test are met. The hypotheses are $H_0: \mu=700$ and $H_a: \mu<700$ at $\alpha=0.05$. The test is completed and the p-value is 0.049. What conclusion is appropriate?
9. Let X be a discrete random variable with a defined probability distribution. Which of the following statements about the probability distribution of X must be true?
10. A veterinarian claims that a lower proportion of dogs will have an upset stomach when fed Diet A compared with Diet B. In a sample of 150 dogs fed Diet A, 18 had an upset stomach; in a separate sample of 160 dogs fed Diet B, 30 had an upset stomach. Which hypotheses are appropriate for a test of this claim?
11. A real estate analyst investigates whether the size of a house in square feet ($x$) explains its sale price in thousands of dollars ($y$) in a large metropolitan area. The analyst believes that, in the population, larger houses tend to sell for more. Which hypotheses are appropriate for testing this claim about the slope in the regression of $y$ on $x$?
12. A company wants to estimate the mean number of sick days employees take per year. Two independent random samples are taken from the same employee population. In Sample 1 (n = 35), the mean is 4.8 sick days; in Sample 2 (n = 35), the mean is 5.6 sick days. Why might the sample results differ?
13. A cafeteria manager recorded the time (in minutes) each of 60 students waited in line during one lunch period, using a stopwatch from when a student joined the line to when they reached the cashier. The dotplot summarizes the wait times. Which feature of the distribution is most evident?
14. A coffee shop owner believes the mean amount of coffee dispensed by a machine is $\mu = 12$ oz. After maintenance, a technician tests $H_0: \mu = 12$ versus $H_a: \mu > 12$ at $\alpha = 0.01$ using a random sample of 40 pours and obtains a p-value of $p = 0.18$. Which interpretation of the p-value is correct?
15. A university tests whether the proportion of applicants who accept an admission offer is different from 0.60 after changing financial-aid packages. They test $H_0: p=0.60$ vs. $H_a: p\neq 0.60$ at $\alpha=0.05$. The university fails to reject $H_0$ and reports no convincing evidence the acceptance rate changed. In reality, the true acceptance rate is $p=0.52$. Which type of error was made?
16. A fitness app company tests whether the mean daily step count for its users is 8,000 steps. A random sample of 100 users is selected, and conditions for a one-sample $t$ test are met. The hypotheses are $H_0: \mu=8000$ and $H_a: \mu\neq 8000$ with $\alpha=0.05$. The test is completed and the p-value is 0.58. What conclusion is appropriate?
17. A school wants to estimate the population mean number of minutes students at the school spend on homework per night, $\mu$. A simple random sample of 60 students is selected, and each student reports their minutes. The point estimate is constructed as the sample mean, $\bar{x}$, computed by adding the 60 reported values and dividing by 60. Which statement describes whether the estimate is biased?
18. A streaming service claims the mean number of minutes users spend per day on its app is $\mu=52$ minutes. Using a random sample of users, a 95% confidence interval for the population mean daily minutes is $(51.0,\ 53.8)$ minutes. Is the claim supported by the confidence interval?
19. A quality-control engineer tests whether the mean fill amount of a cereal box is less than the labeled 500 g. The hypotheses are $H_0: \mu=500$ vs. $H_a: \mu<500$ at $\alpha=0.01$. The test result is to fail to reject $H_0$, so the engineer reports there is not convincing evidence of underfilling. In reality, the true mean fill is $\mu=495$ g (the boxes are underfilled). Which type of error was made?
20. A scatterplot relates the score on a pre-test to the score on a post-test for students in a statistics course. The points are scattered, but generally, students who scored higher on the pre-test also scored higher on the post-test. The relationship, however, is not very tight. The best description would be:

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