Practice Test 69 - AP Statistics

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

Two independent random samples are repeatedly taken to compare average commute times. Each repetition selects $n_1=12$ commuters from City A and $n_2=48$ commuters from City B and computes $\bar{x}_A-\bar{x}_B$ . Assume both population distributions are roughly symmetric with similar spread. Which statement is correct about how changing sample sizes affects the sampling distribution of $\bar{x}_A-\bar{x}_B$ ?
A city council member claims that more than 60% of city residents support a proposed recycling ordinance. A random sample of residents was used to construct a 95% confidence interval for the true population proportion $p$ of residents who support the ordinance: $(0.56,\ 0.64)$ . Is the claim supported by the confidence interval?
An economics student studies $n=30$ used cars and fits a least-squares regression line predicting sale price ( $y$ , dollars) from mileage ( $x$ , thousands of miles). The student's research claim is that, in the population, higher mileage tends to reduce sale price, meaning the population slope is negative. Which hypotheses are appropriate for testing this claim about the slope?
A genetic counselor considers 8 independent births to couples who each have a $0.25$ probability of having a child with a particular recessive trait. Define a success as "the child has the trait." Let $X$ be the number of successes in the 8 births. Which values correctly model this situation with a binomial distribution?
A school district wants to estimate the proportion of all students in grades 9–12 in the district who get at least 8 hours of sleep on a typical school night. A researcher obtained a list of all 9th–12th grade students and used a random number generator to select 300 students to email a short survey. Only 162 students responded, and the researcher used those 162 responses to estimate the district-wide proportion. Which statement best describes the sample representativeness?
A city council wants to know whether support for a new recycling policy is higher among homeowners than renters. In a random sample of 300 homeowners, 201 support the policy. In a random sample of 260 renters, 156 support the policy. A two-proportion $z$ test for $H_0: p_H=p_R$ versus $H_a: p_H>p_R$ gave a p-value of 0.006. At the 5% significance level, what conclusion is appropriate?
In many studies involving inference for the slope of a regression line, the null hypothesis is that the true slope is zero ( $\beta = 0$ ). What is the practical implication if one fails to reject this null hypothesis?
A spinner is divided into 8 equal sections labeled 1 through 8, and it is spun once. Define event $A$ as "the result is 3" and event $B$ as "the result is an odd number." Are the two events mutually exclusive?
A city compared the ages (years) of cars in two neighborhoods: Neighborhood East and Neighborhood West. Five-number summaries are shown below. Which comparison is supported by the display? - East: min 1, $Q_1$ 3, median 6, $Q_3$ 9, max 14; no outliers - West: min 0, $Q_1$ 2, median 4, $Q_3$ 7, max 20; one high outlier at 20
A wildlife researcher set up cameras at one trail for 30 nights to record the most frequently observed animal species each night (categorical variable). The bar chart shows counts of nights: Deer 11, Raccoon 7, Fox 5, Coyote 4, Rabbit 3. Which statement is supported by the graph?
A streaming service randomly samples 2,000 subscribers to estimate the proportion who use the service daily. The company wants to claim that between 45% and 55% of all subscribers use the service daily. A 95% confidence interval for the population proportion is $(0.46, 0.52)$ . Is the claim supported by the confidence interval?
A board game manufacturer claims that a spinner lands on 4 regions with probabilities 0.10, 0.20, 0.30, and 0.40 (Regions A–D). A student spins the spinner 100 times and runs a chi-square goodness-of-fit test at $\alpha=0.05$ . The summary is below. What conclusion is appropriate? Observed/Expected counts and p-value: - A: Observed 16, Expected 10 - B: Observed 18, Expected 20 - C: Observed 29, Expected 30 - D: Observed 37, Expected 40 - p-value = 0.048
A school randomly selects one student and records whether the student is a senior and whether the student plays a sport. Let event $A$ be "the student is a senior" and event $B$ be "the student plays a sport." Some seniors play sports, so the two events can occur together. Are the two events mutually exclusive?
A university wants to determine whether major (STEM vs. Non-STEM) is related to preferred study location (Library, Dorm, Coffee shop). A single random sample of students is surveyed, and each student reports both variables. The counts are shown. Which test is appropriate, and what are the correct hypotheses?
A school principal claims that at least 80% of students at the school eat breakfast before arriving. A random sample was taken and a 90% confidence interval for the true proportion $p$ of students who eat breakfast was computed as $(0.78,\ 0.85)$ . Is the claim supported by the confidence interval?
A fitness app claims that users who follow its plan will have a mean resting heart rate of $\mu=70$ beats per minute after 8 weeks. A researcher believes the mean is lower. A random sample of 35 users completes the plan, and a one-sample $t$ test is run with $H_0:\mu=70$ versus $H_a:\mu<70$ at $\alpha=0.01$ . The p-value is 0.009. What conclusion is appropriate?
A city transportation office wants to compare average commute times between people who drive and people who use public transit. The plan is to interview commuters at a downtown parking garage entrance for three mornings and record commute time and mode of transportation. The research question is: "How do mean commute times compare for all city commuters who drive versus use public transit?" Which aspect is most important to address before collecting data?
A cafeteria tracks the number of pieces of fruit a randomly selected student takes at lunch each day. Let $X$ be this count, a discrete random variable with distribution: $P(X=0)=0.30$ , $P(X=1)=0.45$ , $P(X=2)=0.20$ , $P(X=3)=0.05$ . The mean is $\mu_X=1.00$ fruit and the standard deviation is $\sigma_X=0.84$ fruit. Which interpretation of the mean is correct?
Two independent random samples are taken to compare the proportion of voters who support a ballot measure in two counties. County X: $n_X=60$ ; County Y: $n_Y=60$ . The statistic is $\hat{p}_X-\hat{p}_Y$ . Suppose the true population proportions are $p_X=0.50$ and $p_Y=0.50$ . Over many repetitions, which statement is correct about the sampling distribution of $\hat{p}_X-\hat{p}_Y$ ?
A teacher selects 12 students from a class roster of 24 without replacement and records whether each selected student is left-handed. A success is "left-handed," and exactly 12 students are selected. Does this meet binomial conditions?

Practice tests