Practice Test 67 - AP Statistics

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

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1. A spinner has 8 equal sectors labeled 1 through 8. The spinner is spun once. Let Event $A$ be "the result is even," and Event $B$ be "the result is greater than 6." Which statement about Events $A$ and $B$ is correct?
2. A psychologist compares mean reaction time (in milliseconds) for participants after drinking caffeinated coffee versus decaf. The claim is that caffeine leads to faster reactions on average. A 95% confidence interval for $(\mu_{\text{caffeine}}-\mu_{\text{decaf}})$ is $(-35,\ -5)$. Is the claim supported by the confidence interval?
3. Which of the following describes a continuous random variable rather than a discrete random variable?
4. A high school guidance counselor surveyed 250 graduating seniors about their post-graduation plans. The results showed that 120 plan to attend a four-year college, 75 plan to attend a two-year college, 30 plan to enter the workforce, and 25 are undecided. What is the relative frequency of seniors who plan to attend a four-year college?
5. In a lab, let $X$ be the measurement error (in millimeters) from Device X and $Y$ be the measurement error (in millimeters) from Device Y on the same item. Over many measurements, $\mu_X=0$ with $\sigma_X=1.2$, and $\mu_Y=0$ with $\sigma_Y=0.8$. Assume the errors from the two devices are independent. Define $E=X-Y$. Which statement about $E$ is correct?
6. A university states that exactly 25% of its undergraduates participate in intramural sports. A random sample of 120 undergraduates is surveyed, and 38 report participating ($\hat{p}=0.317$). Which hypotheses are appropriate for assessing whether the university's statement is accurate?
7. A city transportation office wants to investigate the research question: "What proportion of all adult residents in the city support adding protected bike lanes on major streets?" The population is all adult residents of the city. The office posted a link to an online poll on the city's official social media accounts and received 2,450 responses; 71% of respondents said they support adding protected bike lanes. The office concludes that about 71% of all adult residents support adding protected bike lanes. Which statement explains whether the conclusion is valid?
8. Based on this observation, what should the student conclude?
9. A pie chart shows that 25% of students in a school participate in sports, 20% in music, 30% in academic clubs, and 25% in other activities. Which of the following claims is supported by this chart?
10. A university randomly sampled 150 first-year students and found that 63 plan to join at least one campus club. A 92% confidence interval for the true proportion $p$ of all first-year students at the university who plan to join at least one campus club is $(0.35,\ 0.49)$. Which interpretation is correct?
11. A factory has 2,000 bolts in a bin, and 6% are slightly too long. An inspector repeatedly selects many SRSs of $n=150$ bolts without replacement and computes $\hat p$. Which statement about the sampling distribution is correct?
12. A teacher believes students spend more than 30 minutes per night on math homework. A random sample of 35 students reports their nightly math homework time, and a one-sample $t$ test is conducted: $H_0:\mu=30$ vs. $H_a:\mu>30$, with $\alpha=0.05$. The p-value is 0.051. What conclusion is appropriate?
13. A manufacturer claims that exactly 15% of its light bulbs are defective. A quality control team takes a random sample and computes a 90% confidence interval for the true defective proportion $p$: $(0.12,\ 0.18)$. Is the claim supported by the confidence interval?
14. A quality-control inspector tests light bulbs one at a time from a large shipment until finding the first defective bulb. Each test results in either "defective" or "not defective," and the inspector stops as soon as the first defective bulb is found. The inspector wants to model the number of bulbs tested until the first defective bulb is found. Why is a geometric model appropriate for this situation?
15. A hospital wants to estimate the proportion of patients who rate their visit as "excellent." Two independent random samples are taken from the same month's patient list. In Sample 1 (n = 150), 72% rate the visit excellent; in Sample 2 (n = 150), 67% do. Why might the sample results differ?
16. A farm reports the mean weight of its apples is $\mu=150$ grams. A shopper repeatedly selects random samples of $n=10$ apples and computes the sample mean weight $\bar{x}$. Assume the sampling distribution of $\bar{x}$ is approximately normal. Which statement about the sampling distribution is correct?
17. A running shoe company claims that the mean mass of its newest model is 280 grams. A competitor suspects the shoes are actually lighter on average. The competitor buys a random sample of 15 shoes and finds a sample mean mass of 272 grams. Which hypotheses are appropriate for a one-sample test of a population mean shoe mass?
18. A university investigates the research question: "Do first-year students at the university spend more time studying on weekends than on weekdays?" Researchers recruited 40 volunteers from an honors study-skills workshop and had them self-report hours studied on a typical weekday and a typical weekend day; the volunteers reported more hours on weekends. The researchers concluded that first-year students at the university generally study more on weekends than weekdays. Which statement explains whether the conclusion is valid?
19. A social scientist studies whether the number of close friends a person reports ($x$) predicts a loneliness score ($y$), where higher scores mean more lonely. The scientist believes that more close friends is associated with lower loneliness in the population. Which hypotheses are appropriate for testing the claim about the slope in the regression of $y$ on $x$?
20. A teacher models students' quiz scores ($y$, percent) from the number of practice problems completed ($x$) using data from students who completed between 0 and 50 problems. The regression line is $\hat{y}=64+0.6x$. The purpose of the linear model is to describe the relationship and predict typical quiz scores for given practice amounts within the observed range. Which interpretation of the model is correct?

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