Practice Test 49 - AP Statistics

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

Start practice test

1. A university states that the mean time to graduate for its students is $\mu=4.0$ years. A random sample of 50 recent graduates is selected, and a one-sample $t$ test is conducted: $H_0:\mu=4.0$ vs. $H_a:\mu\ne 4.0$, at $\alpha=0.01$. The p-value is 0.018. What conclusion is appropriate?
2. A teacher recorded the scores (out of 20) on a short quiz for all students present in one class period (population: those 26 students). The five-number summary is: min $=7$, $Q_1=12$, median $=15$, $Q_3=17$, max $=20$. A boxplot is drawn. Which feature is consistent with the summary statistics?
3. A gym manager records, for 28 members, the number of minutes they exercise per workout (x) and their resting heart rate (y, beats per minute). The manager is interested in whether exercise time and resting heart rate appear to be related. Do the data suggest the variables are related?
4. A coffee company wants to estimate the proportion of all bags from a large day's production run that are underfilled. Two quality-control technicians each take an independent simple random sample of 120 bags from the same production run. Technician 1 finds 6 underfilled bags (5%), while Technician 2 finds 12 underfilled bags (10%). Why might the sample results differ?
5. An online retailer claims that the long-run distribution of delivery ratings is 60% "On time," 25% "Late," and 15% "Very late." A random sample of 160 deliveries is selected and rated. Observed counts table: On time 102, Late 41, Very late 17 Claimed distribution: (0.60, 0.25, 0.15). Which hypotheses are appropriate for a chi-square goodness-of-fit test?
6. A company has 4 departments with different numbers of employees. To estimate the proportion of all employees who prefer working from home at least 3 days per week, an analyst randomly selected 50 employees from each department (200 total) and found that 55% of those sampled preferred working from home at least 3 days per week. The analyst concluded that "about 55% of all employees prefer working from home at least 3 days per week." Which statement explains whether the conclusion is valid?
7. A website designer claims that 60% of visitors click a certain button. After a random sample of 500 visitors, 286 clicked the button. A one-proportion $z$ test was carried out for $H_0: p=0.60$ versus $H_a: p\neq 0.60$ at $\alpha=0.05$. The test produced a $p$-value of 0.41, so the designer failed to reject $H_0$. Which conclusion is appropriate?
8. A university compares mean GPA for students who attended supplemental instruction sessions (S) versus those who did not (N). A 90% confidence interval for $\mu_S-\mu_N$ is $(0.05,\ 0.30)$. The university claims attendees have a higher mean GPA. Is the claim supported by the interval?
9. A city collected data from 180 residents on whether they commute primarily by car or not and whether they support building more bike lanes. The results are shown. Which comparison is appropriate for assessing whether support for bike lanes is associated with commuting method using conditional distributions? <table> <tr><th></th><th>Support</th><th>Do not support</th></tr> <tr><td>Commute by car</td><td>45</td><td>75</td></tr> <tr><td>Do not commute by car</td><td>42</td><td>18</td></tr> </table>
10. A botanist studies whether the amount of fertilizer applied in grams ($x$) predicts plant height in centimeters after 6 weeks ($y$). The botanist believes that applying more fertilizer increases height in the population (at least in the studied range). Which hypotheses are appropriate for testing this claim about the regression slope?
11. A tech company claims that about 40% of users enable two-factor authentication, meaning the true proportion $p$ is reasonably close to 0.40. A random sample of users produced a 95% confidence interval for $p$ of $(0.41,\ 0.47)$. Is the claim supported by the confidence interval?
12. A political scientist wants to estimate the proportion of registered voters in a county who support a proposed local tax. Two polling organizations each independently take a random sample of 400 registered voters from the same county during the same weekend. Poll 1 reports 48% support, while Poll 2 reports 52% support. Assume both used random sampling and asked the same question. Why might the sample results differ?
13. In a large school district, 65% of students ride the bus to school. A statistician repeatedly takes random samples of $n=400$ students and records $\hat p$, the sample proportion who ride the bus. Which statement about the sampling distribution of $\hat p$ is correct?
14. For the population of newborn weights at a hospital, birth weights are approximately Normal with mean $\mu=3.4$ kg and standard deviation $\sigma=0.5$ kg. The marked value is $x=4.1$ kg. Which statement about the marked value is correct?
15. A nutritionist uses least-squares regression to predict resting heart rate ($y$, beats per minute) from daily caffeine intake ($x$, mg) using data from 52 randomly selected adults. A 99% confidence interval for the population slope is $(0.003, 0.021)$ beats per minute per mg. Which interpretation is correct?
16. An environmental club wants to describe recycling behavior among students at a high school. A random sample of 100 students is asked how often they recycle at home (a categorical variable). The results are shown below. Which statement is supported by the data?

    Recycling frequency	Frequency	Relative frequency
    Always	28	0.280
    Often	34	0.340
    Sometimes	26	0.260
    Never	12	0.120

17. A teacher recorded whether students attended after-school tutoring at least once and whether they passed the final exam. The two categorical variables are Tutoring attendance (Attended/Did not attend) and Final exam result (Passed/Did not pass). Using the two-way table, which comparison is appropriate for assessing whether tutoring is associated with passing? Which comparison is appropriate?
18. A professor claims that students in a flipped classroom format have a higher mean final exam score than students in a traditional format. A 95% confidence interval for $(\mu_{\text{flipped}}-\mu_{\text{traditional}})$ is $( -3,\ 9)$ points. Is the claim supported by this interval?
19. A basketball player takes 20 free throws in practice. Based on long-term data, the player makes a free throw with probability 0.75, and each shot is treated as an independent trial. Let $X$ be the number of made free throws. Which values correctly model this situation with a binomial distribution?
20. A wildlife biologist captures and tags a random sample of 80 fish in a lake and uses the sample to estimate the proportion infected with a parasite. The state will decide whether to restrict fishing based on the estimate. Restrictions can affect local businesses, but failing to restrict could spread disease. Why is it important to consider potential error in the estimate before making the decision?

Practice tests