Practice Test 30 - AP Statistics

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

A librarian tests whether the mean time students spend studying in the library on weeknights is 2 hours. A random sample of 20 students is selected, and conditions for a one-sample $t$ test are met. The hypotheses are $H_0: \mu=2$ and $H_a: \mu\neq 2$ with $\alpha=0.05$ . The test is completed and the p-value is 0.051. What conclusion is appropriate?
A company wants to estimate the proportion of all its employees who would prefer a 4-day workweek. The company surveys 200 employees chosen by a manager who selects "reliable team members who give thoughtful feedback" from across departments. Which issue most threatens the validity of using this sample to represent all employees?
A store tracks the next 45 customers and records whether each customer uses a coupon. A success is "uses a coupon," and exactly 45 customers are observed. A big coupon promotion starts halfway through, increasing coupon use for later customers. Does this meet binomial conditions?
An agriculture researcher wants to study the effects of fertilizer type (Type 1 vs. Type 2) and watering schedule (daily vs. every other day) on tomato yield. The researcher has 40 similar tomato plants and can randomly assign each plant to one fertilizer and one watering schedule for the entire growing season. The researcher is also interested in whether the effect of fertilizer depends on watering schedule. Which experimental design is most appropriate?
A university dining hall records the amounts (in grams) of pasta served in a random sample of $n=58$ lunch plates to model portion sizes and estimate the fraction below a target serving amount. Why is a normal model reasonable in this situation?
An engineer wants to compare the mean battery life (hours) of two brands of rechargeable batteries. The engineer randomly selects 30 batteries of Brand X and 30 batteries of Brand Y from large shipments and tests each battery once under identical conditions. The engineer wants to test whether the mean battery life differs between the two brands. Which inference procedure is most appropriate?
A runner recorded her heart rate (in beats per minute) at the end of each of 45 training runs over a season (population: all 45 recorded heart rates). The five-number summary is: min $=118$ , $Q_1=132$ , median $=145$ , $Q_3=156$ , max $=170$ . A boxplot is made. Which feature is consistent with the summary statistics?
A school counselor models the relationship between hours of sleep the night before an exam ( $x$ ) and exam score ( $y$ ) for a group of students using a least-squares regression line. A scatterplot with the fitted regression line is shown. Which statement about the regression line is correct?
A city measured the amount of water used per household in one month (in hundreds of gallons) for a random sample of 90 households. The summaries were: mean $=62.5$ , median $=58$ , SD $=21.0$ , five-number summary $(18,\ 45,\ 58,\ 74,\ 130)$ , and IQR $=29$ . Which interpretation is correct?
A call center records the number of calls an operator handles in an hour. Let $X$ be the number of calls for a randomly selected operator-hour; $X$ is discrete. The distribution of $X$ has mean $\mu_X=22$ calls and standard deviation $\sigma_X=5$ calls. Which interpretation of the mean is correct?
A school counselor fits a least-squares regression model predicting students' first-semester GPA ( $y$ ) from the number of hours per week spent in a tutoring program ( $x$ ). The counselor claims that each additional tutoring hour increases mean GPA by at least $0.05$ points. A 95% confidence interval for the slope is $(0.02,\ 0.08)$ GPA points per hour. Is the claim supported by the confidence interval?
A streaming service believes that the proportion of users who watch content on a mobile device is different from 35%. The company randomly samples 160 users and finds that 44 primarily watch on mobile ( $\hat{p}=0.275$ ). Which hypotheses are appropriate for testing the company's belief?
A city council uses a random sample survey to estimate support for a proposed property-tax increase to fund road repairs. If they proceed when true support is below 50%, the measure may fail at the ballot and reduce public trust. Why is it important to consider potential error when using the sample estimate to decide whether to place the measure on the ballot?
A city planner records distance from downtown (miles) $x$ and average rent (dollars) $y$ for a sample of apartments, then fits a least-squares regression line to model rent from distance. Which statement about the regression line is correct?
A marketing firm surveyed 500 shoppers about their primary reason for choosing a particular grocery store. The reasons were categorized as Price, Convenience, Quality, and Service. Which of the following graphical displays is most appropriate for visualizing the distribution of these reasons?
A shipment contains many boxes of cereal. A consumer group randomly selects 20 boxes to check a promotional code inside each box. A success is finding a valid code, and the probability a box contains a valid code is $0.95$ (assume independence). Which values of $n$ and $p$ correctly model the number of successes with a binomial distribution?
A fitness app sampled the number of steps taken yesterday by 85 users. The summaries were: mean = 7,900 steps, median = 8,150 steps, SD = 1,600 steps, five-number summary = (min 3,900; $Q_1$ 7,200; median 8,150; $Q_3$ 9,000; max 10,200), and IQR = 1,800 steps. Which interpretation is correct?
In a large city, 52% of registered voters support Candidate A. A pollster repeatedly selects random samples of $n=50$ registered voters and computes the sample proportion $\hat p$ who support Candidate A. Which statement about the sampling distribution of $\hat p$ is correct?
A gym recorded the number of minutes 40 members spent on a treadmill during one visit. The five-number summary (in minutes) is: min $=12$ , $Q_1=20$ , median $=28$ , $Q_3=35$ , max $=58$ . A boxplot is drawn using the standard rule (whiskers extend to the min and max, with no outliers marked). Which feature is consistent with the summary statistics?
A political scientist wants to compare party affiliation across three colleges (College X, Y, Z). Independent random samples of students were selected from each college and classified as Democrat, Republican, or Independent. A chi-square test of homogeneity was performed at $\alpha=0.05$ . The observed counts and p-value are shown. What conclusion is appropriate?

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