Practice Test 54 - AP Statistics

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

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1. A jar contains 3 red and 7 blue marbles. A student wants to estimate the probability that, when drawing 4 marbles without replacement, at least 2 are red. To simulate, the student uses 10 cards labeled R,R,R,B,B,B,B,B,B,B, shuffles, draws the top 4 as one trial, records whether at least 2 are R, replaces the cards, and repeats 400 trials. The student observes 88 successes. Which interpretation of the simulation results is correct?
2. The daily high temperatures (°F) in a certain city during April are approximately Normal with mean $\mu=68$ and standard deviation $\sigma=6$. The normal curve below marks a temperature of 74°F. Which statement about the marked value is correct?
3. A company wants to estimate the proportion of its employees who work remotely at least one day per week. Two independent random samples of 100 employees were selected from the same employee list. In Sample 1, 61 employees reported working remotely at least one day per week; in Sample 2, 55 employees reported the same. The survey question and sampling method were identical. Why might the sample results differ?
4. A hospital tracks whether patients miss a scheduled appointment. Suppose 18 patients are scheduled for appointments on a particular day. Define a success as "the patient misses the appointment." Based on historical data, the probability a scheduled patient misses is $0.15$, and outcomes are treated as independent. Which values correctly model this situation with a binomial random variable $X$ = number of successes?
5. A city claims that calls to its 311 line are distributed by category as follows: Potholes 35%, Trash 25%, Streetlights 20%, Other 20%. A random sample of 400 calls produced the counts below. A chi-square goodness-of-fit test at $\alpha=0.05$ reports $p$-value $=0.03$. What conclusion is appropriate?
6. A researcher studies the relationship between screen time ($x$, in hours per day) and sleep duration ($y$, in hours per night) for 50 teenagers. A 95% confidence interval for the true slope is $(-0.40,\ -0.10)$ hours of sleep per hour of screen time. Which interpretation is correct?
7. The cholesterol levels (mg/dL) for adults in a city are approximately Normal with mean $\mu=190$ and standard deviation $\sigma=25$. The normal curve below marks a cholesterol level of 215 mg/dL. Which statement about the marked value is correct?
8. A grocery store randomly sampled 800 customers to estimate the proportion $p$ of all customers who use reusable bags. In the sample, 264 customers used reusable bags. A 98% confidence interval for $p$ is $(0.30,\ 0.36)$. Which interpretation is correct?
9. A community college wants to estimate the mean number of hours per week that its students spend studying. The college takes a simple random sample of 200 students from the enrollment list and administers a survey. This is an observational study. Which conclusion is justified based on the design of this study?
10. A company tracks the number of customer support tickets received each day for 30 days. The dotplot shows most days between 18 and 26 tickets, but there are two days with 55 and 58 tickets, far from the rest. Which statement best describes the distribution?
11. A gym records the number of minutes 60 members spent on a treadmill during one visit. The dotplot below shows the distribution of times (in minutes). Which statement best describes the distribution? Dotplot counts by minute: - 10: 1 - 12: 1 - 14: 2 - 16: 3 - 18: 4 - 20: 6 - 22: 7 - 24: 8 - 26: 7 - 28: 6 - 30: 5 - 32: 4 - 34: 3 - 36: 2 - 38: 1 (Each count represents how many members had exactly that time.)
12. A school district randomly samples 40 high school students and records the number of minutes they spend on homework on a typical weeknight. A one-sample $t$ interval is computed, and the district reports a 95% confidence interval for the population mean homework time of $(52.1,\ 61.7)$ minutes. Which interpretation is correct?
13. For which value of p will the standard deviation of a binomial distribution be maximized?
14. A relative frequency table for the preferred social media platform of a group of teenagers shows that 0.35 prefer Platform A, 0.25 prefer Platform B, and 0.20 prefer Platform C. If the remaining teenagers in the group prefer Platform D, what is the relative frequency for Platform D?
15. A company tests whether a new website layout increases the proportion of visitors who make a purchase. The explanatory variable is layout (current vs. new), and the response variable is whether a visitor purchases (yes/no). The company randomly assigns incoming visitors to see one of the two layouts and compares purchase rates. Which feature of this study most directly helps ensure that differences in purchase rates are due to the layout rather than preexisting differences between groups of visitors?
16. An environmental scientist studies whether water temperature ($x$, in °C) predicts dissolved oxygen ($y$, in mg/L) in a river. Using 12 measurements taken on randomly selected days, the scientist fits a linear regression of $y$ on $x$ and tests $H_0: \beta_1=0$ versus $H_a: \beta_1<0$. The output gives a one-sided p-value of 0.11. At $\alpha=0.05$, the scientist fails to reject $H_0$. What conclusion is appropriate?
17. A coach wants to know whether practice time ($x$, hours per week) predicts free-throw percentage ($y$) for players on a large team league. Using data from 18 randomly selected players, the coach fits a regression of $y$ on $x$ and performs a slope test: $H_0: \beta_1=0$ vs. $H_a: \beta_1>0$. The one-sided p-value reported is 0.041. At $\alpha=0.05$, the coach rejects $H_0$. What conclusion is appropriate?
18. A city transit agency claims that the proportion of riders who are satisfied with weekend bus service is at least $0.80$. A random sample of $n=250$ riders is surveyed, and $198$ report being satisfied (sample proportion $\hat{p}=0.792$). Which hypotheses are appropriate for a one-proportion test of the agency's claim?
19. A meteorology club investigates whether distance from the coast is related to humidity. The observational units are 30 weather stations. For each station, the club records distance from the coast (in miles), average afternoon relative humidity (percent) for July, and station ID code. The goal is to see if distance from the coast helps explain variation in humidity. Which classification is correct for distance from the coast and relative humidity?
20. A pharmaceutical company tests whether a new drug lowers mean systolic blood pressure compared with 130 mmHg. They test $H_0: \mu=130$ versus $H_a: \mu<130$ at $\alpha=0.01$. They reject $H_0$ and conclude the drug lowers blood pressure. In truth, the drug has no effect and the true mean is still $\mu=130$. Which type of error was made?

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