Practice Test 60 - AP Statistics

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

A student writes down a sequence of 60 coin-flip results from a computer simulation (H for heads, T for tails). The sequence includes several streaks, including one run of 7 H in a row and another run of 6 T in a row, with the rest mixed. The student says "that can't be random because streaks are too long." Under random behavior, you would expect occasional streaks of varying lengths. Is the pattern consistent with random behavior?
A candidate claims that exactly 50% of likely voters support them. A polling organization takes a random sample of 1,000 likely voters and reports a 95% confidence interval for the true support proportion of $(0.47, 0.53)$ . Is the claim supported by the confidence interval?
In a large city, the commute times (in minutes) for all weekday commuters are approximately Normal with mean $\mu=30$ and standard deviation $\sigma=6$ . A particular commuter's time is marked at $x=42$ minutes. Which statement about the marked value is correct?
A school district claims the mean time (in minutes) that students spend on homework each night is $\mu=90$ . A random sample of students was used to construct a 95% confidence interval for $\mu$ , resulting in $(84,\ 96)$ minutes. Is the claim supported by the confidence interval?
A political scientist compared the proportion of registered voters who approve of a policy in two independent random samples. Among 500 voters in Region North, 255 approved; among 450 voters in Region South, 207 approved. A two-proportion $z$ test at $\alpha=0.05$ tested $H_0: p_N=p_S$ versus $H_a: p_N\ne p_S$ , where $p_N$ and $p_S$ are the true approval proportions in the two regions. The p-value was 0.18. What conclusion is appropriate?
A health researcher expects the mean resting heart rate for adults in a certain community to be about 72 beats per minute (bpm). The researcher measures a random sample of 5 adults and finds a sample mean of 81 bpm. The expected behavior is a sample mean near 72, but the observed outcome is higher. Is this result unexpected, given the variability in sample means when the sample size is only 5?
A restaurant owner compares the proportion of customers who rate their experience as "excellent" after two different menu designs are implemented on different weeks. From independent random samples of customers, a 95% confidence interval for the difference in excellent-rating proportions (Week 1 menu minus Week 2 menu) is $( -0.15, -0.02 )$ . Which interpretation is correct?
A company states that 44% of its employees prefer working in the office. Many random samples of $n=36$ employees are taken and $\hat p$ is computed each time. Which statement about the sampling distribution is correct?
A researcher claims the average reaction time for a certain task is $\mu=250$ ms. A random sample of 18 participants is tested, and a one-sample $t$ test is conducted with $H_0:\mu=250$ and $H_a:\mu\neq 250$ at $\alpha=0.10$ . The p-value is 0.095. What conclusion is appropriate?
A university randomly sampled 350 undergraduate students to estimate the proportion $p$ who have taken at least one online course. In the sample, 210 students had taken an online course. A 92% confidence interval for $p$ was reported as $(0.55, 0.65)$ . Which interpretation is correct?
A political analyst believes that in a certain district, 52% of voters support Candidate A. A random sample of 100 likely voters is polled, and 58 say they support Candidate A (58%). The analyst asks whether 58% is surprising due to ordinary sampling variability with $n=100$ if the true support is 52%. Is the result unexpected?
Which of the following is the most appropriate question to formalize this observation for a statistical study?
A city surveyed residents about whether they usually bike to work (Yes/No) and whether they support building more bike lanes (Support/Oppose). The purpose is to compare support rates between bikers and nonbikers using conditional proportions. Which comparison is supported by the data? Counts: Bike: Support 135, Oppose 15 (Total 150). No bike: Support 160, Oppose 40 (Total 200).
The distribution of the number of hours students at a large high school spent on homework last week is unimodal and skewed to the right. Which of the following is a plausible explanation for the shape of this distribution?
A school district compares mean time (minutes) to complete a standardized math test for students who take the test on a computer versus on paper. From independent random samples, a 95% confidence interval for $(\mu_{\text{computer}}-\mu_{\text{paper}})$ is $(0.5,\ 6.0)$ . Which interpretation is correct?
A manufacturer tests whether a new machine produces washers with mean diameter 10.00 mm. The hypotheses are $H_0: \mu = 10.00$ versus $H_a: \mu \ne 10.00$ at $\alpha = 0.05$ . The test result is to fail to reject $H_0$ . In reality, the true mean diameter produced by the machine is 10.00 mm. Which type of error was made?
A gym reports that 85% of members attend at least once per week. A researcher repeatedly takes many random samples of $n=20$ members and computes $\hat p$ . Which statement about the sampling distribution is correct?
A farmer wants a point estimate of the population mean weight $\mu$ of all pumpkins harvested from a large field this week. The farmer takes a simple random sample of 30 pumpkins and computes the sample mean $\bar x$ of their weights, then reports $\bar x$ as the point estimate for $\mu$ . Which statement describes whether the estimate is biased?
A school counselor recorded the number of minutes 36 students spent on homework last night. The dotplot below shows the distribution of times (in minutes). Which statement best describes the distribution?
An environmental scientist wants to investigate whether higher daily air pollution is related to more asthma-related emergency room (ER) visits. She collected data for one year in a city, recording the daily average particulate matter (PM2.5) level and the number of asthma ER visits each day. Days with higher PM2.5 tended to have more asthma ER visits. Which conclusion is justified based on the design of this study?

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