Practice Test 71 - AP Statistics

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

Start practice test

1. A town wants to estimate the proportion of all registered voters in the town who favor a proposed property-tax increase. A polling firm selects a simple random sample of 500 registered voters and mails each a questionnaire. The firm reports results based only on the 190 voters who return the questionnaire. Which issue most threatens the validity of the reported estimate?
2. An online retailer claims that at least 90% of its packages arrive on time. A random sample of 300 recent shipments shows 261 arrived on time (so $ \hat{p}=261/300$). A consumer advocate wants to test whether the true on-time rate is below the claim. Which hypotheses are appropriate?
3. A card app assumes that each dealt card is equally likely from a standard 52-card deck. A user wants to estimate the probability that, in 5 cards dealt without replacement, at least one is an ace. The user simulates 5000 deals using a random-number generator that shuffles a virtual deck each trial, deals 5 cards, and records whether at least one ace appears. The simulation produced 1690 deals with at least one ace. Which interpretation of the simulation results is correct?
4. A hospital tests whether the mean waiting time in the emergency room is less than 30 minutes after adding staff. They test $H_0: \mu=30$ vs. $H_a: \mu<30$ at $\alpha=0.05$. They fail to reject $H_0$ and state there is not convincing evidence the mean waiting time is below 30 minutes. In reality, the true mean waiting time is $\mu=30$ minutes. Which type of error was made?
5. A community center wants to compare the proportion of residents who would attend a free weekend class if it were offered in the morning versus the afternoon. The plan is to call residents whose phone numbers are listed in the community center's membership database and ask whether they would attend a morning class or an afternoon class. The research question is: "For all residents in the community, is the proportion willing to attend different for morning versus afternoon?" Which aspect is most important to address before collecting data?
6. What was the predicted first-year college GPA for this student according to the model?
7. An economist wants to test whether the linear relationship between years of education and annual income is positive among full-time workers in a state. A random sample of 60 workers is selected, and for each worker the economist records years of education (quantitative) and annual income (quantitative). Which inference procedure is most appropriate to test whether the population slope is greater than 0?
8. A sports scientist investigates whether mean vertical jump height differs between athletes who follow Program 1 and those who follow Program 2. Two independent random samples were taken (Program 1: $n=12$; Program 2: $n=14$). A two-sample $t$ test for $\mu_1-\mu_2$ was conducted with $H_0:\mu_1-\mu_2=0$ and $H_a:\mu_1-\mu_2\neq 0$. The p-value was 0.049. Using $\alpha=0.05$, what conclusion is appropriate?
9. A grocery store records whether a shopper uses a digital coupon (event $D$) and whether the shopper buys the store-brand cereal (event $C$). The coupon is specifically for the store-brand cereal, so coupon users may be more likely to buy it. How does knowing that a shopper used a digital coupon ($D$ occurred) affect the likelihood that the shopper bought the store-brand cereal ($C$)?
10. A teacher compares mean quiz scores for students who used Method A vs Method B. She randomly assigns students to methods, then takes an SRS of $n_1=30$ Method A scores and an independent SRS of $n_2=30$ Method B scores from the larger classes and computes $\bar{x}_A-\bar{x}_B$. Over many repetitions of this sampling process, which statement is correct?
11. A pharmaceutical company conducts a randomized clinical trial to test whether a new medication reduces migraine frequency compared with a placebo. Regulators will consider approval if the trial provides evidence of effectiveness. If the inference is wrong, patients could be exposed to side effects without benefit, or a helpful drug could be delayed. Why is it important to consider potential error when interpreting the trial's statistical conclusion?
12. A lab technician measures the diameter (in millimeters) of a simple random sample of $n=70$ ball bearings produced by a machine and wants a model to estimate the proportion outside a tolerance range. Why is a normal model reasonable for the diameters?
13. A nutrition teacher wants to test whether eating a high-protein breakfast improves attention in first-period class. She recruits 72 students who usually skip breakfast. On Monday, she randomly assigns half to eat a provided high-protein breakfast and half to eat a provided low-protein breakfast. During first period, the teacher records each student's attention score using a standardized rubric (0–20); this score is the response variable. Which aspect of the design is an example of control?
14. A meteorologist investigates whether atmospheric pressure ($x$) predicts wind speed ($y$) on 28 randomly selected days. The meteorologist fits a linear regression of wind speed on pressure and performs a slope test with $H_0: \beta_1=0$ versus $H_a: \beta_1\neq 0$. The two-sided p-value is 0.051. Using $\alpha=0.05$, the meteorologist fails to reject $H_0$. What conclusion is appropriate?
15. A textbook publisher claims that the mean weight of its hardcover calculus book is 4.5 pounds. A university bookstore manager wants to check if the mean weight is actually different, because shipping costs depend on weight. A random sample of 20 books has a sample mean weight of $\bar{x}=4.62$ pounds. Which hypotheses are appropriate for a test about the population mean book weight $\mu$?
16. A student records the random variable $X$, the number of text messages received in an hour. From a long period of observation, the distribution of $X$ has mean $\mu_X=3.2$ and standard deviation $\sigma_X=1.6$. Which interpretation of the mean is correct?
17. A psychologist randomly samples 22 adults and measures their score on a stress scale. A one-sample $t$ interval is used, and a 92% confidence interval for the population mean stress score is $(18.3,\ 21.6)$. Which interpretation is correct?
18. A company reports that 38% of calls to customer service are resolved on the first call. A supervisor repeatedly takes many random samples of $n=200$ calls and computes $\hat p$. Which statement about the sampling distribution is correct?
19. A bookstore manager records how many customers purchase a membership in a given hour. Let the discrete random variable $X$ be the number of memberships purchased during a randomly selected hour. The probability distribution of $X$ is shown in a table. Which statement correctly interprets the random variable $X$?
20. A psychologist claims that the proportion of participants who report high stress is lower among those who practice daily meditation than among those who do not. In a random sample of 220 daily meditators, 46 reported high stress; in a separate random sample of 210 non-meditators, 62 reported high stress. Which hypotheses are appropriate for a test of this claim?

Practice tests