Practice Test 85 - AP Statistics

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

The lifetimes of a certain brand of LED bulbs (in thousands of hours) are approximately Normal with mean $\mu=30$ and standard deviation $\sigma=4$ . The normal curve below marks the interval 26 to 34 thousand hours. Which statement about the marked interval is correct?
For the population of all SAT Math scores in a state, scores are approximately Normal with mean $\mu=520$ and standard deviation $\sigma=80$ . A score of 680 is marked on the normal curve. Which statement about the marked value is correct?
A company compares customer satisfaction (Satisfied/Not Satisfied) between three store locations (North, Central, South). A random sample of customers from each location is surveyed and the results are summarized in a $3\times 2$ table of counts. The company wants to know whether satisfaction depends on location. Which inference procedure is most appropriate?
A website shows an advertisement to 25 randomly selected visitors. For each visitor, define a success as the visitor clicking the ad. Assume each visitor's click behavior is independent and the probability of a click is $0.08$ . Let $X$ be the number of clicks among the 25 visitors. Which values correctly model this situation with a binomial distribution (identify $n$ and $p$ )?
A pharmaceutical company tests whether the mean reduction in blood pressure from a new drug exceeds 5 mmHg. They use $H_0: \mu=5$ versus $H_a: \mu>5$ at $\alpha=0.05$ . The test is not statistically significant, so they conclude there is not enough evidence the mean reduction exceeds 5 mmHg. In reality, the true population mean reduction is $\mu=6$ mmHg. Which type of error was made?
A wildlife researcher measured the body mass (in kg) of every adult female in a small herd of 35 deer (population: all adult females in that herd). The five-number summary is: min $=42$ , $Q_1=48$ , median $=53$ , $Q_3=57$ , max $=66$ . A boxplot is constructed. Which feature is consistent with the summary statistics?
A hospital tests whether a new discharge checklist reduces 30-day readmissions. The explanatory variable is checklist type (new vs. current), and the response variable is whether a patient is readmitted within 30 days. The hospital has two wards; Ward 1 uses the new checklist for all patients and Ward 2 uses the current checklist for all patients for three months. Which design principle is most clearly violated, making it difficult to attribute differences in readmission rates to the checklist?
A school district wants to compare the proportion of students who prefer online homework in two middle schools. An SRS of $n_1=150$ students is taken from School 1 and an independent SRS of $n_2=150$ students is taken from School 2. The statistic $\hat{p}_1-\hat{p}_2$ is computed. If the sampling is repeated many times, the distribution of $\hat{p}_1-\hat{p}_2$ will have a mean of $p_1-p_2$ and a standard deviation that decreases as the sample sizes increase. Which statement is correct?
An online retailer compares two website layouts. Layout X was shown to a random sample of 400 visitors, and 92 made a purchase. Layout Y was shown to a separate random sample of 380 visitors, and 78 made a purchase. A two-proportion $z$ test for $H_0: p_X=p_Y$ versus $H_a: p_X<p_Y$ produced a p-value of 0.91. At the 1% significance level, what conclusion is appropriate?
A fitness company completed an experiment to compare two warm-up routines (Dynamic vs. Static) on 1-mile run time. The company recruited 80 volunteers from its own gym. Each volunteer was randomly assigned to perform either the Dynamic or Static warm-up, then immediately ran 1 mile on the same indoor track. The Dynamic group had a faster mean time. Which conclusion is justified based on the design of this study?
An environmental scientist randomly samples 30 locations along a river and measures nitrate concentration (mg/L). A one-sample $t$ interval gives a 90% confidence interval for the population mean nitrate concentration of $(3.2,\ 4.0)$ mg/L. Which interpretation is correct?
A random sample of 12 different days was selected, and the amount of rainfall (in inches) was recorded for each day in a region. A 90% confidence interval for the population mean daily rainfall was $(0.18, 0.34)$ inches. Which interpretation is correct?
A researcher compares the proportion of patients who report side effects for two medications using independent random samples. For Medication X, 28 of 80 patients report side effects; for Medication Y, 18 of 75 patients report side effects. A 92% confidence interval for $p_X - p_Y$ is $(0.02,\ 0.24)$ . Which interpretation is correct?
A jar contains 6 red marbles and 4 blue marbles. A student draws marbles without replacement until exactly 5 marbles have been drawn. A draw is a success if the marble is red. The student records the number of red marbles drawn. Does this meet binomial conditions?
A city surveys residents about support for building a new park. In a random sample, 198 of 300 residents in Neighborhood 1 support the park and 176 of 320 residents in Neighborhood 2 support the park. A 90% confidence interval for $p_1 - p_2$ is $(0.04,\ 0.18)$ . A council member claims that support is higher in Neighborhood 2 than in Neighborhood 1. Is the claim supported by the confidence interval?
A city compares the proportion of commuters who use public transit in two districts. District East: 132 transit users out of 220 commuters; District West: 140 transit users out of 220 commuters. A 95% confidence interval for $p_{East}-p_{West}$ is $(-0.12,\ 0.04)$ . A planner claims that public transit use is higher in the West district than in the East district. Is the claim supported by the confidence interval?
A game uses a spinner with three outcomes: Red (probability 0.5), Blue (probability 0.3), and Green (probability 0.2). A player wins if, in 5 spins, Green occurs at least twice. To estimate the probability of winning, a student runs 4000 simulated games. In each game, she generates 5 random digits (0–9) and maps 0–4 to Red, 5–7 to Blue, and 8–9 to Green, then checks whether Green occurred at least twice. The simulation produced 426 wins. Which interpretation of the simulation results is correct?
A librarian records the number of books checked out by each of 65 patrons in a month. The five-number summary (books) is: min $=0$ , $Q_1=2$ , median $=4$ , $Q_3=7$ , max $=12$ . A boxplot is drawn using these values. Which feature is consistent with the summary statistics?
A school compares the proportion of students who prefer online homework in Grade 9 versus Grade 10. A 95% confidence interval for the difference in proportions, defined as $p_9 - p_{10}$ , is $(0.04, 0.18)$ . A student claims, "Grade 9 has a higher proportion of students who prefer online homework than Grade 10." Is the claim supported by the confidence interval?
A school cafeteria manager claims that students choose among four lunch options in the following proportions: 35% pizza, 30% salad, 20% sandwich, and 15% pasta. On a randomly selected day, a random sample of 200 students is recorded with the observed counts below. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the manager's claim?

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