Practice Test 57 - AP Statistics

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

A company tests whether a new website layout increases the time users spend on a product page. The explanatory variable is layout (new vs. old), and the response variable is time on page in seconds. The company randomly assigns each of 10,000 site visitors to see either the new or old layout during a single visit. Which statement best describes what random assignment accomplishes in this context?
A manufacturer tests whether the mean lifetime of a battery is greater than 8 hours. They test $H_0: \mu=8$ vs. $H_a: \mu>8$ at $\alpha=0.05$ . The test result is to reject $H_0$ and claim the mean lifetime exceeds 8 hours. In reality, the true mean lifetime is $\mu=8.6$ hours. Which type of error was made?
A delivery company tracks daily packages. Let $X$ be the number of packages delivered by Driver 1 in a day and $Y$ be the number delivered by Driver 2 in a day. Over many days, $\mu_X=95$ with $\sigma_X=20$ , and $\mu_Y=105$ with $\sigma_Y=25$ . Assume $X$ and $Y$ are independent. Define $S=X+Y$ . Which statement about $S$ is correct?
Which of the following is the best interpretation of $P(X=0) = 0.60$ ?
A website runs an A/B test in which 30 visitors are each shown the same version of a landing page. A success is defined as "the visitor clicks the sign-up button." From prior experiments, the click probability for a visitor shown this version is $0.12$ , and visitor outcomes are treated as independent. Which values correctly model this situation with a binomial random variable $X$ = number of successes?
A researcher collected data from 25 college students on weekly hours of exercise ( $x$ ) and resting heart rate in beats per minute ( $y$ ). A linear regression of $y$ on $x$ was fit, and a slope test was performed with $H_0: \beta_1=0$ versus $H_a: \beta_1\neq 0$ . The computer output reported a negative estimated slope and a p-value of 0.012. Using a 5% significance level, the researcher must decide whether there is evidence of a linear association between exercise hours and resting heart rate in this sample. What conclusion is appropriate?
A community garden coordinator asks: "Does providing weekly text-message reminders increase the number of volunteer hours?" The population is all registered volunteers. The plan is to send reminders only to volunteers who have previously volunteered at least twice (because their phone numbers are already on file) and then compare their volunteer hours to those of volunteers without reminders. Which aspect is most important to address before collecting data?
Two farms measured the weights (pounds) of apples harvested in a season. The distributions are summarized with five-number summaries. Which comparison is supported by the display? - Farm 1: min 0.20, $Q_1$ 0.28, median 0.32, $Q_3$ 0.36, max 0.45; no outliers - Farm 2: min 0.18, $Q_1$ 0.27, median 0.32, $Q_3$ 0.35, max 0.60; one high outlier at 0.60
A city compares the proportion of households that recycle weekly in two neighborhoods. Neighborhood 1: SRS of $n_1=100$ households; Neighborhood 2: independent SRS of $n_2=100$ households. The statistic is $\hat{p}_1-\hat{p}_2$ . Which statement is correct about the standard deviation of the sampling distribution of $\hat{p}_1-\hat{p}_2$ ?
A marketing agency claims that fewer than 50% of adults in a certain county use a particular social media platform. A random sample of 60 adults is selected to test this claim. What is the complete, correct setup for this significance test?
A student flips a coin 30 times and records whether each flip is heads. A success is "heads," and the student plans exactly 30 flips. Does this meet binomial conditions to model the number of successes?
A university compares the proportion of students who prefer in-person office hours versus virtual office hours in two departments. In random samples, 96 of 150 students in Department M prefer in-person, and 88 of 160 students in Department N prefer in-person. A 90% confidence interval for $p_M - p_N$ is $(0.01,\ 0.21)$ . A student claims that Department N has a higher preference for in-person office hours than Department M. Is the claim supported by the confidence interval?
A trainer at a gym wants to investigate if there is a positive linear relationship between the number of hours a person spends at the gym per week and the amount of weight they can lift. Data is collected from a random sample of gym members. From an inferential standpoint, what is the fundamental question the trainer is trying to answer?
A principal wants to estimate the mean number of hours of sleep students at a large high school get on school nights. Two independent random samples of 40 students each were taken from the same school. Sample A reported a mean of 6.7 hours, and Sample B reported a mean of 7.2 hours. Both surveys were administered the same way and asked about "last night's sleep." Why might the sample results differ?
A company tests two versions of a website to see which leads to more purchases. In a randomized experiment, Version 1 is shown to 500 visitors and Version 2 to 520 visitors. A 99% confidence interval for the difference in purchase rates (Version 1 minus Version 2) is $(-0.06, -0.01)$ . Which interpretation is correct?
A wildlife biologist wants to estimate the proportion of fish in a lake that are longer than 30 cm. Two different random samples are taken using the same method on the same weekend. In Sample A (n = 100), 28% are longer than 30 cm; in Sample B (n = 100), 35% are longer than 30 cm. Why might the sample results differ?
Two independent random samples are taken from two populations of reaction times (ms). Sample 1 has size $n_1=15$ and sample 2 has size $n_2=15$ . The statistic of interest is $\bar{x}_1-\bar{x}_2$ . Which statement is correct about the sampling distribution of $\bar{x}_1-\bar{x}_2$ ?
A shipping company tracks the number of days a package takes to arrive. The population distribution of delivery times is left-skewed (most packages take 3–5 days, but a few arrive unusually fast). A manager repeatedly takes random samples of $n=50$ packages and computes the sample mean delivery time $\bar{x}$ . He examines the sampling distribution of $\bar{x}$ . Why is the sampling distribution approximately normal?
A student investigates whether screen time (hours per day) is related to sleep duration (hours per night). The scatterplot shows a fairly tight downward linear pattern. Which statement about correlation is correct?
A marketing team wants to know whether device type is related to whether a customer completes an online purchase. From a random sample of site visits, each visit was classified by device (Phone, Tablet, Computer) and outcome (Purchase, No purchase). A chi-square test of independence was performed at the $\alpha=0.05$ level. The observed counts and p-value are shown. What conclusion is appropriate?

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