Practice Test 34 - AP Statistics

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

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1. A gym owner believes that more than 35% of members attend at least 3 times per week. To check, a random sample of 160 members is selected, and 49 report attending at least 3 times per week (so $ \hat{p}=49/160$). Which hypotheses are appropriate for a one-proportion $z$ test of the owners belief?
2. A nonprofit is comparing two fundraising email subject lines to see if one leads to a higher donation rate. From a random sample of 500 recipients who received Subject Line 1, 65 donated ($\hat{p}_1=0.13$). From an independent random sample of 480 recipients who received Subject Line 2, 48 donated ($\hat{p}_2=0.10$). The research claim is that Subject Line 1 leads to a higher donation rate. Which hypotheses are appropriate?
3. A test of $H_0:p=0.08$ uses $n=80$. Which condition fails?
4. A basketball player takes 30 free throws. The sequence of makes (M) and misses (X) contains a repeating pattern: M, X, M, X, M, X, repeating exactly for all 30 shots. Under random behavior, you might see short alternations, but exact repeating patterns over many trials are not expected. Is the pattern consistent with random behavior?
5. A city wants to estimate the mean number of minutes commuters wait for a bus during weekday mornings. Two independent simple random samples of 50 weekday commuters are taken from the same set of routes during the same month. Sample 1 has a mean wait time of 7.8 minutes; Sample 2 has a mean wait time of 9.1 minutes. Why might the sample results differ?
6. For the population of diameters of ball bearings produced by a factory, diameters are approximately Normal with mean $\mu=10.00$ mm and standard deviation $\sigma=0.04$ mm. The marked interval is from $9.92$ mm to $10.08$ mm. Which statement about the marked interval is correct?
7. Two brands of batteries (Brand X and Brand Y) were tested for lifetime (hours) until failure. A side-by-side boxplot summary is given by five-number summaries below. Which comparison is supported by the display? - Brand X: min 6, $Q_1$ 10, median 14, $Q_3$ 18, max 22; no outliers - Brand Y: min 4, $Q_1$ 9, median 13, $Q_3$ 17, max 19; no outliers
8. For a chi-square test of independence, which of the following comparisons between expected counts is correct?
9. A researcher interviews households until finding 12 households that agree to participate in a study. For each household contacted, a success is "agrees to participate" and a failure is "does not agree." The researcher records the number of households contacted to reach 12 successes. Does this meet binomial conditions for modeling the number of successes?
10. A delivery company randomly samples 45 packages and estimates the mean delivery time (in days). A 95% confidence interval for the population mean delivery time is $(2.9, 3.4)$ days. The company advertises that the true mean delivery time is 3.0 days. Is the claim supported by the confidence interval?
11. A wildlife camera records an animal sighting each night as one of {Deer, Raccoon, No animal}. Let N be the event that no animal is recorded. The park ranger states $P(N)=0.40$. Which statement correctly describes the probability?
12. A city planner expects that about 60% of residents support building a new bike lane. A random sample of 50 residents is surveyed, and 24 say they support it (48%). The planner expected the sample proportion to be near 60%, but the observed outcome is lower. Is the result unexpected, given the variability in random sampling with a sample size of 50?
13. A student plots the results of 40 spins of a fair spinner that lands Red or Blue with equal chance. The plot (in order) shows many short runs, with totals Red = 18 and Blue = 22, and no obvious repeating cycle. Under random behavior, you'd expect roughly equal totals with some variation and no systematic pattern over time. Is the pattern consistent with random behavior?
14. What is the probability that a randomly selected watch has at least two defects?
15. A gym wants to estimate the mean number of visits per month for all gym members. The manager surveys members who are present at the gym on Saturday afternoon and asks how many times they visited in the past month. The manager reports the sample mean as the average for all members. Which issue most threatens the validity of this conclusion?
16. A botanist measures $n=25$ plants of the same species and uses linear regression to predict plant height ($y$, cm) from hours of sunlight per day ($x$). The botanist claims that, in the population, additional sunlight increases average height, so the population regression slope is positive. Which hypotheses are appropriate for testing this claim about the slope?
17. A school district records the heights in inches of a random sample of 75 ninth-grade students. Height is influenced by many small genetic and environmental factors, and the distribution is roughly symmetric with one peak. Why is a normal model reasonable for these heights?
18. A company wants to answer: "Do employees who work from home at least 3 days per week report higher job satisfaction?" The population is all employees at the company. The proposed plan is to survey employees about job satisfaction and categorize them by whether they currently work from home at least 3 days per week, then compare average satisfaction scores. Which aspect is most important to address before collecting data?
19. A public health researcher compared the proportion of adults who received a flu shot in two counties. In random samples, 130 of 200 adults in County A and 96 of 180 adults in County B reported receiving a flu shot. A 90% confidence interval for $p_A - p_B$ is $(0.04,\ 0.18)$. Which interpretation is correct?
20. A counselor meets with 14 students and records whether each student reports feeling stressed. A success is "stressed," and exactly 14 students are interviewed. The counselor selects students from the same close friend group, so responses may influence each other. Does this meet binomial conditions?

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