Practice Test 89 - AP Statistics

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

A state park wants to estimate the proportion of visitors who would recommend the park to a friend. Two independent random samples are taken from the same visitor log for a holiday weekend. In Sample A (n = 150), 88% would recommend; in Sample B (n = 150), 82% would recommend. Why might the sample results differ?
A streaming service tests whether a new recommendation algorithm increases the mean number of hours watched per week from 6 hours. The hypotheses are $H_0: \mu = 6$ and $H_a: \mu > 6$ . At $\alpha = 0.05$ , the analysts fail to reject $H_0$ . In reality, the algorithm truly increases the mean to $\mu = 6.5$ . Which type of error was made?
What is the corresponding percentage for students majoring in Business?
A school district tests whether a new tutoring program increases the mean math score compared with the historical mean of 72 points. They test $H_0: \mu=72$ versus $H_a: \mu>72$ at $\alpha=0.05$ . They fail to reject $H_0$ and decide not to expand the program. In reality, the tutoring program truly increases performance and the true mean score under the program is $\mu=75$ . Which type of error was made?
A company tests whether a new training program changes mean weekly sales compared with the old program. A random sample of 30 employees used the new program and a separate random sample of 28 employees used the old program. A two-sample $t$ test for $\mu_{new}-\mu_{old}$ was conducted with hypotheses $H_0: \mu_{new}-\mu_{old}=0$ and $H_a: \mu_{new}-\mu_{old}>0$ . The test produced a p-value of 0.018. Using $\alpha=0.05$ , what conclusion is appropriate?
A nutrition researcher compares the mean daily sodium intake (in milligrams) for adults who follow Diet X and adults who follow Diet Y. A random sample of 50 adults on Diet X had a mean intake of 2,180 mg, and a random sample of 47 adults on Diet Y had a mean intake of 2,320 mg. The research claim is that Diet X results in a lower mean sodium intake than Diet Y. Which hypotheses are appropriate for a two-sample $t$ test comparing population means?
A health clinic wants to estimate the mean waiting time (in minutes) for patients on weekday mornings. Two independent simple random samples were taken from the same set of weekday mornings during the same month. Sample 1 (n = 25) had a mean waiting time of 18.4 minutes; Sample 2 (n = 25) had a mean of 21.1 minutes. The same definition of "waiting time" was used. Why might the sample results differ?
A manufacturer measures the diameters (in mm) of a random sample of 80 ball bearings from a day's production to check process consistency. The sample histogram is roughly symmetric and mound-shaped. Why is a normal model reasonable for describing ball bearing diameters here?
A city planner wants to estimate the mean commute time (in minutes) for all workers in a city. A random sample of 100 workers yields a 95% confidence interval for the population mean commute time of $(27.4, 31.8)$ minutes. Which interpretation is correct?
A researcher wants a point estimate of the population proportion $p$ of voters in a state who support a new policy. The researcher calls 400 landline phone numbers selected from a directory and computes $\hat p$ from those who answer and agree to respond, then reports $\hat p$ as the point estimate for $p$ . Which statement describes whether the estimate is biased?
In a binomial setting with n=25 and failure probability 0.4, what is the standard deviation?
An engineer tests whether the amount of insulation in an attic ( $x$ , measured in inches) predicts a home's monthly heating cost ( $y$ , in dollars) during winter. Data from 30 similar homes are collected and a least-squares regression of heating cost on insulation thickness is fit. The engineer claims that adding insulation decreases average heating cost, so the population slope should be negative. Which hypotheses are appropriate for a one-sided test of the slope?
For the population of students taking a certain final exam, scores are approximately Normal with mean $\mu=78$ and standard deviation $\sigma=6$ . The instructor marks a score of 66 as a concern. Which statement about the marked value is correct?
In a town, 55% of adults own a car, 35% own a bicycle, and 20% own both. Let Event A be "randomly selected adult owns a car" and Event B be "randomly selected adult owns a bicycle." Which statement about Events A and B is correct?
A restaurant owner claims that exactly 50% of customers order takeout rather than dining in. A random sample of customers produced a 95% confidence interval for the true proportion $p$ who order takeout: $(0.47,\ 0.53)$ . Is the claim supported by the confidence interval?
An environmental agency tests whether the mean concentration of a pollutant in a river exceeds the legal limit of 10 ppm. The hypotheses are $H_0: \mu=10$ versus $H_a: \mu>10$ , and the test uses $\alpha=0.01$ . The p-value is 0.009. Which interpretation of the p-value is correct?
A university wants to estimate the proportion of all undergraduate students who support extending library hours. The university obtains a complete list of all undergraduates and uses a random number generator to select 400 students to contact. Of those selected, 220 respond. The university uses only the 220 responses to estimate the proportion. Which statement best describes the sample representativeness?
A game app awards a daily login bonus that is randomly one of three types: {Coins, Gems, Energy}. Let G be the event that the bonus is Gems. The app's help page states $P(G)=0.10$ for a randomly selected day. Which statement correctly describes the probability?
A student randomly selects one book from a shelf of 60 books. There are 22 fiction books (F), 18 hardcover books (H), and 9 books that are both fiction and hardcover. Let Event A be "the selected book is fiction" and Event B be "the selected book is hardcover." Which statement about Events A and B is correct?
A psychologist wants to estimate the mean score on a stress questionnaire for employees at a large company. A random sample of 45 employees is taken, and a 95% confidence interval for the population mean stress score is $(31.0, 35.8)$ . Which interpretation is correct?

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