Practice Test 48 - AP Statistics

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

A sociologist repeatedly takes random samples of size 40 from a large population of workers to study the relationship between years of education and annual income. For each sample, the slope of the least-squares regression line is calculated. Which of the following best describes the resulting collection of all the calculated sample slopes?
A factory tests 15 smartphones from the same production line and records whether each phone passes a drop test. A success is "passes," and exactly 15 phones are tested, but the phones are tested in order of production and the machine gradually wears out during testing, reducing pass rates over time. Does this meet binomial conditions?
For one cell, its row total doubles, column total triples, table total doubles. What happens to expected count?
The expected count for a cell in a two-way table for a chi-square test of independence can be interpreted as the expected number of observations in that cell if the null hypothesis is true. This is equivalent to which of the following?
An airline randomly samples 80 flights on a route and estimates the mean departure delay (in minutes). A 95% confidence interval for the population mean delay is $(8.5, 12.1)$ . A news report claims the true mean delay is 8 minutes. Is the claim supported by the confidence interval?
A streaming service tests whether the proportion of users who finish a new series differs between two age groups. An independent random sample of $n_1=150$ users ages 18–34 and $n_2=150$ users ages 35+ is selected, and $\hat p_1$ and $\hat p_2$ are the sample proportions who finish the series. Consider the sampling distribution of $\hat p_1-\hat p_2$ across repeated sampling. Which statement is correct?
A student recorded the number of hours studied ( $x$ ) and the score on a quiz out of 100 ( $y$ ) for 12 classmates (hours ranged from 0.5 to 6). A least-squares regression line was fit to predict quiz score from hours studied: $\hat{y} = 52 + 6.5x$ . The purpose of this linear model is to summarize the linear association and predict typical quiz scores for study times within the observed range. Which interpretation of the model is correct?
Two different researchers are studying the same population to determine the linear relationship between age and blood pressure. Researcher A takes a random sample of 50 individuals, and Researcher B takes a different random sample of 50 individuals. Both calculate the least-squares regression line. Which statement is most likely to be true?
A biologist models plant height (cm) from the amount of fertilizer applied (grams). The biologist claims that more fertilizer is associated with an increase in mean plant height. A 92% confidence interval for the slope is $( -0.3,\,1.7)$ cm per gram. Is the claim supported by the confidence interval?
A lab device should randomly label samples as "Control" (C) or "Treatment" (T). Over 26 samples, the labels in order are: C T T C C T C C T T C T C T C C T C T T C C T C T C. Under random labeling you would expect a mixture with some short runs and no strict alternation or repeating block. Is the pattern consistent with random behavior?
An internet provider claims the mean download speed for customers on a plan is $\mu=200$ Mbps. A random sample of customers is tested and a 95% confidence interval for $\mu$ is found to be $(201,\ 214)$ Mbps. Is the claim supported by the confidence interval?
A driver approaches traffic lights along a route and notes each light as green or not green upon arrival. The driver continues until encountering the first red light. Assume each light encountered is independent and the probability a light is red upon arrival is constant. The driver records the number of lights encountered until the first red light. Why is a geometric model appropriate?
A school district wants to predict students' end-of-year math exam score (points) from the number of hours each student spent using an online practice system during the semester. Using data from a random sample of 80 students, the district fits a least-squares regression of exam score (response) on practice hours (explanatory). The district's research claim is that more practice hours are associated with higher average exam scores in the population, meaning the population regression slope is positive. Which hypotheses are appropriate for testing this claim about the slope?
A company claims its light bulbs last an average of 1000 hours. A consumer group tests $H_0: \mu=1000$ vs. $H_a: \mu\neq1000$ at $\alpha=0.01$ . The p-value is 0.18, so they fail to reject $H_0$ and report there is not convincing evidence the mean lifetime differs from 1000 hours. In reality, the true mean lifetime is $\mu=950$ hours. Which type of error was made?
A nutritionist wants to compare the mean sodium content (in mg) of two brands of canned soup. A random sample of 30 cans from Brand A had a mean sodium content of 690 mg, and a random sample of 28 cans from Brand B had a mean of 720 mg. The research claim is that Brand A has a lower mean sodium content than Brand B. Which hypotheses are appropriate?
A manufacturing company tests a random sample of 60 batteries from a day's production and finds 4 are defective. Management considers shutting down the line to recalibrate machines, which is costly; however, failing to recalibrate could send defective batteries to customers and create safety risks. Why is it important to consider potential error?
A county election office wanted to know whether voters prefer to receive election reminders by text message or by email. From the county's list of registered voters, the office randomly selected 1,000 voters and sent each selected voter a survey asking their preferred reminder method. Which conclusion is justified based on the design of this study?
A restaurant owner claims that fewer than 10% of customers wait more than 15 minutes for a table on weekends. A random sample of 200 weekend customers produces a 95% confidence interval for the true proportion who wait more than 15 minutes of $(0.09, 0.13)$ . Is the claim supported by the confidence interval?
A company tests two versions of an email subject line and records the proportion of recipients who open the email. Version 1 was sent to 400 recipients and 112 opened it; Version 2 was sent to 380 recipients and 133 opened it. A 99% confidence interval for $p_1 - p_2$ is $(-0.15,\ -0.02)$ . A marketing analyst claims that Version 2 has a higher open rate than Version 1. Is the claim supported by the confidence interval?
A charity call center defines $X$ as the number of donations received in a randomly selected hour. The distribution of $X$ has mean $\mu_X=9.5$ donations and standard deviation $\sigma_X=2.7$ donations. Which interpretation of the standard deviation is correct?

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