Practice Test 32 - AP Statistics

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

A wildlife biologist studies whether the amount of rainfall in a month ( $x$ ) predicts the number of insects counted in a field survey ( $y$ ). The biologist suspects that more rainfall leads to more insects in the population. Which hypotheses are appropriate for testing this claim about the slope of the population regression line predicting $y$ from $x$ ?
A clinic records whether a patient received a flu vaccine this season (event $V$ ) and whether the patient later tested positive for influenza (event $I$ ). Vaccination is expected to reduce the chance of influenza. How does knowing that a patient was vaccinated ( $V$ occurred) affect the likelihood that the patient tested positive ( $I$ )?
A company tracks the number of seconds it takes a computer to boot. Boot times are approximately Normal with mean $\mu=42$ s and standard deviation $\sigma=6$ s. Which comparison is supported without computing any exact probabilities?
A state agency wants to estimate the mean weekly hours of exercise for all adults in the state. The agency draws a simple random sample of 1,000 adults from a list of registered voters and calls them. Many selected adults do not answer after multiple attempts, and the agency uses only the completed interviews. Which issue most threatens the validity of the estimate?
A teacher investigates whether the number of absences predicts final exam score (out of 100) using a random sample of 30 students. A 95% confidence interval for the slope is $(-3.2,\ -0.6)$ points per absence. Which interpretation is correct?
A teacher records, for a random sample of 28 students, the number of practice problems completed ( $x$ ) and the score on a quiz ( $y$ , percent). A least-squares regression line predicts quiz score from problems completed. A 90% confidence interval for the true slope is $(0.10,\ 0.55)$ percentage points per problem. Which interpretation is correct?
A coffee shop chain wants to know whether changing the background music to a slower tempo increases the average amount customers spend per visit. The chain selected 20 of its 200 stores by taking the 20 stores closest to its headquarters. The 20 stores were randomly assigned: 10 stores played slow-tempo music for two weeks and 10 stores kept their usual music. The slow-tempo stores had higher average spending. Which conclusion is justified based on the design of this study?
A political analyst tests whether a candidate's true support among likely voters is greater than 50%. The hypotheses are $H_0: p = 0.50$ versus $H_a: p > 0.50$ with $\alpha = 0.05$ . Using a random sample poll, the analyst fails to reject $H_0$ and reports there is not convincing evidence the candidate is above 50%. In reality, the candidate's true support is exactly 50%. Which type of error was made?
An environmental group compares mean nitrate level (mg/L) in water samples taken upstream (U) versus downstream (D) of a factory. A 95% confidence interval for $\mu_U-\mu_D$ is $(-0.8,\ -0.1)$ . The group claims the mean nitrate level is higher downstream than upstream. Is the claim supported by the interval?
A hospital researcher studies whether insurance type is related to length of stay. For each patient discharged from the medical ward in one month, the researcher records insurance type coded 1 = private, 2 = Medicare, 3 = Medicaid, 4 = uninsured and length of stay (in days). The goal is to compare lengths of stay across insurance types. Observational units are the patients. Which classification is correct?
A school counselor wants to study whether students who sleep more tend to have higher GPAs. A random sample of 60 students reports average hours of sleep per night ( $x$ ) and current GPA ( $y$ ). The counselor plans to fit the least-squares regression line predicting GPA from sleep. The research claim is that more sleep is associated with a higher predicted GPA (a positive slope). Which hypotheses are appropriate for testing this claim about the population regression slope?
A city transportation department recorded the primary commute mode for a convenience sample of 200 riders entering a downtown area during one morning (categorical variable). The bar chart shows counts: Car 96, Bus 54, Train 28, Bike 14, Walk 8. Which statement is supported by the graph?
A coffee shop manager believes the average wait time for a drink during the morning rush is about 4 minutes. On one randomly selected morning, the manager records the wait times for 8 customers and finds an average of 6.5 minutes. The manager expected the sample mean to be near 4 minutes, but the observed mean was higher. Is the result unexpected, considering the variability of sample means from small random samples?
A school district wants to know whether a new after-school tutoring program increases end-of-semester math scores. Two similar high schools are selected; one school implements tutoring for all Algebra I students and the other continues as usual. At the end of the semester, a random sample of 40 Algebra I students from each school is taken and their exam scores (0–100, quantitative) are recorded. Which inference procedure is most appropriate to assess whether the tutoring program changes the mean score?
A public health agency randomly samples 1,100 residents to estimate the proportion who received a flu shot this season. The agency wants to claim that at least 65% of residents received a flu shot (that is, $p\ge 0.65$ ). A 95% confidence interval for the population proportion is $(0.62, 0.66)$ . Is the claim supported by the confidence interval?
A plant scientist tests whether fertilizer A increases tomato yield compared with fertilizer B. She has 40 similar tomato plants in a greenhouse. She numbers the plants 1–40 and uses a random number generator to assign 20 plants to fertilizer A and 20 to fertilizer B. After 8 weeks, she measures yield in grams per plant. Which is the explanatory variable in this experiment?
A school district collected data from a random sample of 32 high schools relating average weekly homework time (hours, $x$ ) to average SAT Math score ( $y$ ). A least-squares regression line was fit to predict $y$ from $x$ . A 95% confidence interval for the true slope of the regression line is $(4.2,\ 11.6)$ SAT points per hour. Which interpretation is correct?
In a state, 52% of registered voters are affiliated with Party A. Suppose many random samples of $n=400$ voters are taken and $\hat p$ is computed each time. Which statement about the sampling distribution is correct?
A voter outreach group claims that 25% of registered voters in a county are undecided in an upcoming election. A random sample of 500 registered voters finds 105 undecided. A one-sample proportion test is run at $\alpha=0.05$ with hypotheses $H_0:p=0.25$ and $H_a:p<0.25$ . The test gives a $p$ -value of 0.01, so the decision is to reject $H_0$ . Which conclusion is appropriate?
The mean score on a certain professional exam is $\mu=520$ . A test-prep company repeatedly takes random samples of $n=64$ exam scores and computes the sample mean $\bar{x}$ . Assume the sampling distribution of $\bar{x}$ is approximately normal. Which statement about the sampling distribution is correct?

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