Practice Test 42 - AP Statistics

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

A researcher claims a computer is generating random points in time (in seconds) between 0 and 60 for event alerts. In one minute, 12 alert times are recorded: 2, 7, 11, 18, 23, 29, 34, 41, 46, 52, 57, 59. Under random behavior you would expect some irregular gaps, including occasional clusters and occasional larger gaps, not nearly evenly spaced times. Is the pattern consistent with random behavior?
A pharmaceutical company is testing a new drug and is concerned that the proportion of patients experiencing a particular side effect is greater than the 3% rate of the current standard drug. Which set of hypotheses is most appropriate for their significance test?
A school district wants to know whether fewer than 30% of high school students get at least 8 hours of sleep on school nights. In a random sample of 150 students, 38 report getting at least 8 hours. A one-sample $z$ test for a population proportion is performed with $H_0: p=0.30$ and $H_a: p<0.30$ at $\alpha=0.10$ . The $p$ -value is 0.12, so the null hypothesis is not rejected. Which conclusion is appropriate?
A school compares the proportion of students who prefer online homework between two grade levels. A random sample of 180 ninth-graders and 200 tenth-graders was taken, and a 95% confidence interval for the difference in proportions (ninth minus tenth) was computed as $(0.04, 0.18)$ . Which interpretation is correct?
A bottling plant wants to verify that the mean fill volume of a drink is 500 mL. A random sample of 24 bottles is measured, and a one-sample $t$ test is performed with $H_0: \mu = 500$ mL and $H_a: \mu \ne 500$ mL at $\alpha=0.05$ . The p-value is 0.046. What conclusion is appropriate?
A streaming service claims that the long-run distribution of subscription types among its customers is 55% Basic, 30% Standard, and 15% Premium. A random sample of 200 current customers is selected, and their subscription types are recorded as shown. Observed counts table: Basic 96, Standard 73, Premium 31 Claimed distribution: (0.55, 0.30, 0.15). Which hypotheses are appropriate for a chi-square goodness-of-fit test?
A city compares the proportion of households that recycle regularly in two neighborhoods. Independent random samples were taken, and a 95% confidence interval for the difference in recycling proportions (Neighborhood 1 minus Neighborhood 2) is $(0.12, 0.25)$ . Which interpretation is correct?
A teacher compares the mean score on a final exam for students in two different class sections. A random sample of 26 students from Section 1 had a mean score of 78.5, and a random sample of 24 students from Section 2 had a mean score of 81.2. The teacher's research claim is that Section 2 has a higher population mean exam score than Section 1. Which hypotheses are appropriate for a two-sample $t$ test comparing population means?
A county reports that 72% of homes have high-speed internet. Many random samples of $n=64$ homes are taken and $\hat p$ is computed each time. Which statement about the sampling distribution is correct?
A cereal company claims the prizes in its boxes are equally likely to be 1 of 4 types (A, B, C, D). A consumer group randomly selects 200 boxes and records the prize type. A chi-square goodness-of-fit test is performed to test $H_0$ : the distribution is uniform across the 4 types versus $H_a$ : the distribution is not uniform. The test output gives a p-value of 0.032. The observed and expected counts are shown in a table. What conclusion is appropriate at the $\alpha=0.05$ level?
A city official wants to display the sources of city tax revenue for the past year. The sources are Property Tax, Sales Tax, Income Tax, and Other Fees. Which of the following graphs would be best to emphasize each source's contribution to the total revenue?
A teacher tests whether the mean score on a standardized math test for students in her district is greater than the national mean of 500. A random sample of 60 students is selected, and conditions for a one-sample $t$ test are met. The hypotheses are $H_0: \mu=500$ and $H_a: \mu>500$ with $\alpha=0.05$ . The test is completed and the p-value is 0.004. What conclusion is appropriate?
A quality-control inspector tests exactly 40 light bulbs from a shipment by turning each one on for 5 seconds. A bulb is counted as a success if it lights immediately; otherwise it is a failure. The inspector selects bulbs one at a time without replacement from a very large shipment made by the same machine on the same day. Does this situation meet the conditions for using a binomial model to describe the number of successes?
Which of the following conclusions is supported by the residual plot?
Two different study methods are compared for the proportion of students who earn an A on a final exam. A 98% confidence interval for the difference in proportions, defined as $p_{Method1} - p_{Method2}$ , is $(0.05,\ 0.20)$ . A teacher claims, "Method 2 results in a higher A rate than Method 1." Is the claim supported by the confidence interval?
A museum director claims that more than 35% of visitors are from out of town. Based on a random sample of visitors, an 88% confidence interval for the population proportion of out-of-town visitors is $(0.31, 0.36)$ . Is the claim supported by the confidence interval?
A delivery service recorded the number of packages delivered per route in one day for 55 routes. The summaries were: mean $=98$ , median $=95$ , standard deviation $=15$ , five-number summary (min $=60$ , $Q_1=88$ , median $=95$ , $Q_3=106$ , max $=140$ ), and IQR $=18$ . Which interpretation is correct?
A company tested a new website layout to see if it increases the proportion of visitors who make a purchase. Over one week, the company randomly assigned each site visitor (in real time) to see either the current layout (control) or the new layout (treatment). At the end of the week, the company compared purchase rates between the two groups of visitors. Which conclusion is justified based on the design of this study?
A survey organization knows that 30% of households in a region have a pet cat. Many random samples of $n=20$ households are selected, and for each sample the statistic $\hat p$ (the sample proportion with a cat) is recorded. Which statement about the sampling distribution of $\hat p$ is correct?
A restaurant chain wants to estimate the proportion of all customers nationwide who would recommend the chain. The company selects 20 restaurants by choosing the 20 locations closest to the corporate headquarters and surveys every customer who makes a purchase during one weekday lunch period at those locations. Which statement best describes the sample representativeness?

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