Practice Test 99 - AP Statistics

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

A teacher gives a 5-question true/false quiz to a student who guesses on every question. A response is counted as correct (success) or incorrect (failure). Assume each guess is independent and that the probability of a correct guess on any question is 0.50. Let $X$ be the number of correct answers out of 5. Which values correctly model this situation?
A city engineer is estimating the mean daily water usage (in gallons) for households in a small city. A random sample of 60 households was selected, and a 99% confidence interval for the population mean daily water usage was computed as $(280,\ 340)$ gallons. Which interpretation is correct?
A university claims that at most 30% of first-year students take a gap year before enrolling. A random sample is taken and a 98% confidence interval for the true proportion $p$ is $(0.29,\ 0.36)$ . Is the claim supported by the confidence interval?
Let $Y$ be a discrete random variable representing the number of text messages a student receives during a 30-minute class period. The distribution of $Y$ has mean $\mu_Y=3.4$ and standard deviation $\sigma_Y=2.1$ . Which interpretation of the standard deviation is correct?
A city's daily pollen count (grains per cubic meter) has a population distribution that is bimodal due to seasonal patterns and is not close to normal. A random sample of $n=80$ days from several years is selected, and the mean pollen count is computed. Why is the sampling distribution of the sample mean approximately normal?
A professor wants to test whether allowing students to use a one-page notes sheet improves quiz performance. She has two sections of the same course taught back-to-back. She flips a coin to decide that the first section may use a notes sheet (treatment) and the second section may not (control). Both sections take the same quiz; the response variable is quiz score. Which factor is a potential confounder that could make it difficult to attribute differences in scores solely to the notes-sheet policy?
Historically, a certain genetic trait appears in 15% of a plant population. A biologist has developed a new hybrid and wants to determine if the proportion of plants with this trait has changed. A significance test will be conducted. Let $p$ be the proportion of plants with the trait in the new hybrid population. What are the appropriate hypotheses?
A psychologist investigates whether average hours of sleep differ between teenagers who have a later school start time (L) and those with an earlier start time (E). Independent random samples are taken, and a two-sample $t$ test for $\mu_L-\mu_E$ uses $H_0: \mu_L-\mu_E=0$ and $H_a: \mu_L-\mu_E\neq 0$ . The p-value is 0.074. Using $\alpha=0.05$ , what conclusion is appropriate?
A teacher recorded whether 150 students attended after-school tutoring at least once this month and whether they passed the most recent quiz. The two-way table is shown. Which comparison is appropriate for determining whether quiz outcome is associated with tutoring attendance using conditional distributions? <table> <tr><th></th><th>Passed</th><th>Did not pass</th></tr> <tr><td>Tutoring</td><td>48</td><td>12</td></tr> <tr><td>No tutoring</td><td>60</td><td>30</td></tr> </table>
A school compares the proportion of students who prefer online homework in two grades. In a random sample, 78 of 120 ninth-graders and 64 of 130 tenth-graders said they prefer online homework. A 95% confidence interval for the difference in population proportions, $p_9 - p_{10}$ , is $(0.06,\ 0.26)$ . Which interpretation is correct?
A restaurant owner believes that more than 15% of customers order dessert. Over one randomly selected week, a random sample of 160 customers is surveyed and 33 report ordering dessert. A one-sample proportion test is performed at $\alpha=0.05$ with hypotheses $H_0:p=0.15$ and $H_a:p>0.15$ . The test yields a $p$ -value of 0.021, so the decision is to reject $H_0$ . Which conclusion is appropriate?
A restaurant chain reports that 70% of customers rate their experience as "satisfied" or "very satisfied." A random sample of 150 customers is surveyed, and 96 give a satisfied rating ( $\hat{p}=0.64$ ). Which hypotheses are appropriate for determining whether the reported proportion is accurate?
A wildlife agency estimates the population size of an endangered species using a statistical method based on a sample of sightings and then decides whether to restrict hiking access to protect habitat. Why is it important to consider potential error in the estimate when making this decision, given tradeoffs between conservation benefits and public access?
A city wants to estimate the mean amount residents spend on public transportation each month. The population is all adult residents of the city. A student stands outside a downtown subway station from 7–9 AM on Monday and asks every 5th person exiting the station to report their monthly spending; 220 people are surveyed. Which statement best describes the sample representativeness?
A company wants to estimate the proportion of all employees at its headquarters who are satisfied with the cafeteria food. The company posts a link to an online survey on the internal homepage and reports results from the 540 employees who chose to respond. Which statement best describes the sample representativeness?
A company tests two website designs and measures mean time-on-page. They compute a 95% confidence interval for the difference in population means, $\mu_A-\mu_B$ , as $(-12,\ 3)$ seconds. A manager claims: "Design A keeps users on the page longer on average than Design B." Is the claim supported by the confidence interval?
An online retailer claims that orders are shipped using three carriers in these proportions: 50% Carrier A, 30% Carrier B, and 20% Carrier C. A random sample of 250 recent orders is selected and the observed counts are shown below. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the retailer's claim?
A student investigates whether there is a linear relationship between the number of hours spent studying for a final exam and the exam score. The student collects data from a random sample of 35 students in the course, recording study hours (quantitative) and exam score (quantitative). Which inference procedure is most appropriate to assess whether the slope of the least-squares regression line differs from 0?
In a region, the daily high temperature (in $^\circ$ F) in July is approximately Normal with mean $\mu=88$ and standard deviation $\sigma=5$ . An interval is marked: from $x=78$ to $x=98$ $^\circ$ F. Which statement about the marked interval is correct?
A school counselor investigates whether hours of sleep on a school night helps explain first-period quiz score. For each student in a random sample of 80 ninth graders, the counselor records the number of hours the student slept last night and the student's quiz score (out of 20) in first period today. The observational units are the students. Which classification is correct?

Practice tests