Practice Test 20 - AP Statistics

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

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1. A city is evaluating whether installing LED streetlights reduces the proportion of nighttime traffic accidents. In a random sample of 180 intersections with LED lights, 27 had a nighttime accident in the past year ($\hat{p}_L=0.15$). In an independent random sample of 200 intersections with traditional lights, 44 had a nighttime accident ($\hat{p}_T=0.22$). The research claim is that LED lights reduce the accident rate. Which hypotheses are appropriate?
2. A hospital researcher studies whether patient age helps predict readmission status. For each of 150 discharged patients (observational units), the researcher records age in years and whether the patient was readmitted within 30 days (yes/no). The goal is to see if age is associated with readmission. Which classification is correct?
3. A marketing team sampled 28 stores and recorded amount spent on local advertising ($x$) and weekly revenue ($y$). A least-squares regression of $y$ on $x$ was fit. The slope test used $H_0: \beta_1=0$ vs. $H_a: \beta_1\ne 0$ and produced a p-value of 0.003 with a positive estimated slope, so the team rejected $H_0$ at $\alpha=0.05$. What conclusion is appropriate?
4. A school reports that 40% of students play a sport, 30% are in band, and 15% do both. Let Event A be "a randomly selected student plays a sport" and Event B be "the student is in band." Which statement about Events A and B is correct?
5. A public health official claims that fewer than 10% of adults in a region smoke cigarettes. A random sample was used to compute a 98% confidence interval for the true proportion $p$ of adults who smoke: $(0.09,\ 0.12)$. Is the claim supported by the confidence interval?
6. The time (in minutes) it takes the population of customers to complete an online checkout is approximately Normal with mean $\mu=8.0$ minutes and standard deviation $\sigma=1.5$ minutes. The marked value is $x=5.0$ minutes. Which statement about the marked value is correct?
7. A local news station wants to estimate the proportion of all adults in the county who support a proposed sales-tax increase. During the evening broadcast, the station asks viewers to text YES or NO, and it reports the results from the 8,500 texts received. Which issue most threatens the validity of the station's conclusion?
8. A researcher draws exactly 12 cards from a well-shuffled standard 52-card deck without replacement. A success is drawing a heart; a failure is drawing a non-heart. The researcher wants to model the number of hearts drawn using a binomial distribution. Does this meet binomial conditions?
9. A psychologist samples $n=27$ adults and fits a regression model predicting stress score ($y$) from hours of sleep per night ($x$). The psychologist claims that, in the population, more sleep is associated with lower stress (negative slope). Which hypotheses are appropriate for testing this claim about the population regression slope?
10. A public health researcher randomly sampled 500 adults in a county to estimate the proportion $p$ who received a flu shot this year. In the sample, 275 adults reported receiving a flu shot. A 95% confidence interval for $p$ was found to be $(0.51, 0.59)$. Which interpretation is correct?
11. A university compares the proportion of students who attend at least one tutoring session in a semester among commuters versus on-campus residents. A 95% confidence interval for the difference in proportions, defined as $p_{commuter} - p_{resident}$, is $(-0.09, 0.02)$. A student claims, "Commuters attend tutoring at a higher rate than residents." Is the claim supported by the confidence interval?
12. A city council wants to know whether a majority of residents support building a new public library. A random sample of 200 residents found that 118 support the plan. A one-proportion $z$ test was conducted for $H_0: p=0.50$ versus $H_a: p>0.50$ at significance level $\alpha=0.05$. The test produced a $p$-value of 0.028, so the council rejected $H_0$. Which conclusion is appropriate?
13. A survey asked 300 office workers to state their preferred type of office plant. The responses were categorized as Flowering, Succulent, Foliage, and No Preference. If a bar chart is created to represent the data, what would the labels on the horizontal axis represent?
14. A school district wants to estimate the proportion of all high school students who would support starting classes 30 minutes later. Two different students each take an independent simple random sample of 120 students from the same district roster. Sample 1 finds 62% support, while Sample 2 finds 54% support. Why might the sample results differ?
15. The athletic department of a university collects data on the heights (in inches) and weights (in pounds) of all its varsity athletes. This dataset is best described as:
16. For a chi-square test, what is the sum of the expected counts for the 'Under 30' age group across all three vacation types?
17. A basketball player takes 18 free throws in practice. A success is making a free throw, and the player's long-run free-throw percentage is $0.75$ (assume each shot is independent). Which values of $n$ and $p$ correctly model the number of made free throws with a binomial distribution?
18. A website runs an A/B test by showing Version A of a page to each of the next 200 visitors. For each visitor, a success is defined as the visitor clicking the "Buy" button. The marketing team wants to model the number of successes among the 200 visitors with a binomial distribution. Does this meet binomial conditions?
19. A hospital records the systolic blood pressure (in mmHg) of a simple random sample of 55 adult patients at routine visits and wants to estimate the proportion with unusually high systolic pressure. Why is a normal model reasonable for systolic blood pressure in this context?
20. A sports scientist recruited 40 volunteer runners from a local running club to test whether a new stretching routine reduces 5K race times. The 40 volunteers were randomly assigned to either use the new routine or continue their usual warm-up for 6 weeks, then each ran a timed 5K. The new-routine group had a lower mean time. Which conclusion is justified based on the design of this study?

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