Practice Test 38 - 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 a typical school night. Two different classes each take an independent simple random sample of 80 students from the same district list. The first sample reports 46% get at least 8 hours, and the second sample reports 55%. Why might the sample results differ?
2. An article reports only the percentage in each category. Which graph of this categorical variable can be made exactly?
3. A hospital screens 18 patients for a certain condition. Each patient's test result is recorded as positive or negative. Suppose the probability a randomly selected patient tests positive is $0.12$, and test outcomes for different patients are treated as independent. Let $X$ be the number of positive tests. Which values correctly model this situation with a binomial distribution (identify $n$ and $p$)?
4. A nurse administers a new vaccine to exactly 80 patients. A success is that a patient reports a fever within 24 hours; a failure is no fever. The nurse notes that patients are from the same household groups, so reactions among family members may be correlated. Does this meet binomial conditions for the number of patients with fever?
5. A doctor compared the proportion of patients who experience a side effect for two medications using independent random samples. For Medication M, 26 of 130 patients had the side effect; for Medication P, 18 of 120 patients had the side effect. A two-proportion $z$ test at $\alpha=0.05$ tested $H_0: p_M=p_P$ versus $H_a: p_M\ne p_P$, where $p_M$ and $p_P$ are the true side-effect proportions for the two medications. The p-value was 0.28. What conclusion is appropriate?
6. A company compares mean battery life (hours) for two phone models, Model X and Model Y. A 95% confidence interval for $\mu_X-\mu_Y$ is reported as $(-1.6,\ 0.9)$. The company claims Model X has longer mean battery life than Model Y. Is the claim supported by the interval?
7. A streaming service claims that among its users, the distribution of preferred movie genres is 35% action, 25% comedy, 20% drama, and 20% sci-fi. A random sample of 180 users is asked for their preferred genre; results are shown in a table. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the service's claim?
8. A student randomly draws one card from a well-shuffled standard 52-card deck and records whether it is a heart or not a heart. Let event $H$ be "the card is a heart," so $P(H)=\frac{13}{52}=0.25$. Which statement correctly describes the probability $P(H)=0.25$?
9. A company wants to estimate the mean job satisfaction score (1–10) for all employees. The HR department selects a simple random sample of 200 employees and asks them to complete a satisfaction survey in a group meeting led by their direct managers, who can see who turns in each survey. Which issue most threatens the validity of the results?
10. A library tracks the genres of books checked out by patrons. A relative frequency table shows the following: Fiction: 0.52, Non-Fiction: 0.28, Young Adult: 0.15. The rest are Children's books. If 400 books were checked out in total, what is the frequency of Children's books?
11. An environmental group claims that more than 35% of households in a county compost food scraps. A survey produced a 95% confidence interval for the true proportion $p$ of households that compost: $(0.31,\ 0.36)$. Is the claim supported by the confidence interval?
12. A school claims that students choose among 5 lunch options with equal frequency. A student randomly records the lunch choice of 150 students on one day and obtains the counts shown in a table. A chi-square goodness-of-fit test is conducted for $H_0$: all 5 options are equally likely vs. $H_a$: not all options are equally likely. The p-value is 0.62. What conclusion is appropriate at the $\alpha=0.05$ level?
13. A cafeteria manager randomly selects one customer and defines a discrete random variable $X$ as the number of pieces of fruit the customer buys (0, 1, 2, or 3). The probability distribution of $X$ is shown in a table. Which statement correctly interprets the random variable?
14. A school district recorded the number of minutes 120 high school students spent on homework last night. The summaries were: mean = 62.4 min, median = 55 min, SD = 28.1 min, five-number summary = (min 10, $Q_1$ 40, median 55, $Q_3$ 75, max 160), and IQR = 35 min. Which interpretation is correct?
15. To conduct a chi-square test for homogeneity, what is the expected number of patients in the treatment group who would show improvement if the treatment had no effect compared to the placebo?
16. A student connects bar tops in a bar chart of unordered categories. The main problem is that the line
17. In a region, the distribution of monthly household electricity use (in kWh) is approximately Normal for the population of all households. The mean is $\mu=900$ kWh with standard deviation $\sigma=150$ kWh. The value 1050 kWh is marked on the normal curve. Which statement about the marked value is correct?
18. A public health researcher compared the proportion of adults who received a flu shot in two counties. In a random sample of 250 adults from County 1, 155 reported getting a flu shot; in a random sample of 220 adults from County 2, 110 reported getting a flu shot. A two-proportion $z$ test was conducted for $H_0: p_1=p_2$ versus $H_a: p_1>p_2$, and the p-value was $0.018$. Using $\alpha=0.05$, what conclusion is appropriate?
19. A coffee shop owner wants to estimate the mean amount (in ounces) of coffee dispensed by a machine. She randomly selects 50 cups and computes a 99% confidence interval for the population mean amount dispensed: $(11.6, 12.4)$ ounces. Which interpretation is correct?
20. A school district wants to know whether a new text-message reminder system changes the proportion of parents who attend parent-teacher conferences. Two similar middle schools are chosen: one uses reminders (n = 180 parents invited) and the other does not (n = 200 parents invited). Attendance is recorded as Yes/No, and the counts are 108 Yes in the reminder school and 90 Yes in the no-reminder school. Which inference procedure is most appropriate to determine whether the reminder system is associated with a different attendance rate?

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