Practice Test 50 - AP Statistics

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

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1. The distribution of individual commute times in a large city is not normal; it is right-skewed due to occasional traffic jams. A researcher repeatedly takes random samples of $n=80$ commuters and computes the sample mean commute time $\bar{x}$. The sampling distribution of $\bar{x}$ is approximately normal. Why is the sampling distribution approximately normal?
2. A public health student studies whether smoking status is associated with resting heart rate. In a survey, each participant reports smoking status (Never, Former, Current) and has resting heart rate measured in beats per minute. The observational units are participants, and the goal is to compare heart rates among smoking-status groups. Which classification is correct?
3. A table reports athletes 80, musicians 50, neither 30, for 120 students. Counts sum to 160. The table is invalid because...
4. A university randomly sampled 250 undergraduate students and found that 160 said they prefer taking exams on a computer rather than on paper. A 99% confidence interval for the true proportion $p$ of all undergraduates at the university who prefer computer-based exams is $(0.55,\ 0.73)$. Which interpretation is correct?
5. A factory's historical defect rate is $p=0.02$. An engineer repeatedly selects random samples of $n=25$ items from a very large day's production and computes $\hat p$, the sample proportion defective. Which statement about the sampling distribution of $\hat p$ is correct?
6. A school nurse checks 35 students for fever and records whether each student has a fever (temperature at least 100.4F). A success is "has fever," and exactly 35 students are checked. Does this meet binomial conditions to model the number with fever?
7. A hospital administrator tests whether the mean waiting time in the emergency room is less than 30 minutes after a new triage system is implemented. A random sample of 45 patients is selected, and conditions for a one-sample $t$ test are met. The hypotheses are $H_0: \mu=30$ and $H_a: \mu<30$ at $\alpha=0.05$. The test is completed and the p-value is 0.013. What conclusion is appropriate?
8. A charity reports that 5% of mailed donation requests receive a response. Many random samples of $n=500$ requests are considered, and $\hat p$ is the sample proportion that receive a response. Which statement about the sampling distribution is correct?
9. A city transportation department selects a simple random sample of 120 intersections from all intersections in the city and records whether each has a functioning pedestrian "walk" signal. In the sample, 102 intersections have a functioning signal. Which conclusion is supported by these data?
10. A botanist tests whether three fertilizers lead to different distributions of plant growth categories. She randomly assigns plants to Fertilizer A, B, or C, then classifies growth after 8 weeks as Low, Medium, or High. The results are shown below. A chi-square test of homogeneity is performed and gives $p<0.001$. What conclusion is appropriate? Two-way table (counts):

    Fertilizer	Low	Medium	High
    A	25	40	15
    B	10	35	35
    C	30	30	20

11. A company compares mean time (minutes) to assemble a product using Tool X versus Tool Y. Two independent random samples yield a 95% confidence interval for $(\mu_X-\mu_Y)$ of $(-6.0,\ -1.5)$ minutes. Which interpretation is correct?
12. A nutritionist compares two diets by repeatedly selecting independent random samples: $n_1=30$ people on Diet A and $n_2=50$ people on Diet B, then computing the difference in sample mean weight loss, $\bar{x}_A-\bar{x}_B$. Which statement is correct about the mean of the sampling distribution of $\bar{x}_A-\bar{x}_B$?​
13. A psychologist fits a regression line predicting stress score from hours of sleep per night for a random sample of adults. A 95% confidence interval for the population slope is $(-2.8,\ -0.4)$. Which interpretation is correct?
14. A university wants to compare the distribution of majors for its male and female undergraduate students. While two pie charts could be used, why is a side-by-side bar chart often considered a better choice for this comparison?
15. A university wants to estimate the proportion of all undergraduate students who have used the campus mental health center in the past year. Administrators email a survey to 2,000 randomly selected undergraduates; only 420 students respond after three reminders. Which issue most threatens the validity of using the 420 responses to estimate the campus-wide proportion?
16. An environmental group claims that the proportion of households that recycle weekly is different in neighborhoods with curbside pickup than in neighborhoods with drop-off only. A random sample of 180 households in curbside neighborhoods found 126 recycle weekly, and a separate random sample of 160 households in drop-off-only neighborhoods found 96 recycle weekly. Which hypotheses are appropriate for a test of this claim?
17. A school counselor collects data from 12 students on weekly study time ($x$, hours) and their quiz score ($y$, points). A least-squares regression line is fit to predict quiz score from study time, with equation $\hat{y}=58+3.2x$. The purpose of this linear model is to summarize the linear association and predict typical quiz scores for students with study times similar to those observed. Which interpretation of the model is correct?
18. A principal asked a random sample of 140 teachers which grade level they primarily teach (categorical variable). The bar chart shows counts: Grade 9: 29, Grade 10: 34, Grade 11: 41, Grade 12: 26, Mixed grades: 10. Which statement is supported by the graph?
19. A tech company tracks call lengths. Let $X$ be the length (in minutes) of a support call handled by Agent 1 and $Y$ be the length (in minutes) of a support call handled by Agent 2. Assume $X$ and $Y$ are independent, with $\mu_X=14$, $\sigma_X=4$, $\mu_Y=16$, and $\sigma_Y=3$. Define $G=X+Y$, the total minutes for two calls (one per agent). Which statement about $G$ is correct?
20. A retailer randomly sampled 600 recent customers and found that 102 made a purchase using a mobile wallet. A 95% confidence interval for the true proportion $p$ of all recent customers who used a mobile wallet is $(0.14,\ 0.20)$. Which interpretation is correct?

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