Practice Test 17 - AP Statistics

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

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1. A streaming service studies whether subscription plan is related to weekly viewing time. The observational units are individual subscribers selected at random. For each subscriber, the service records plan code (1 = Basic, 2 = Standard, 3 = Premium), total hours watched last week, and device type most used. The goal is to see if the plan helps explain variation in hours watched. Which classification is correct for plan code and hours watched?
2. A manufacturer samples 30 screws from a very large shipment and records whether each screw meets the length specification. A success is "meets spec," and exactly 30 screws are checked. Does this meet binomial conditions to model the number of successes?
3. A chemist studies whether the concentration of a reactant in mol/L ($x$) predicts the reaction rate in mol/(L·s) ($y$). The chemist claims that higher concentration increases reaction rate in the population. Which hypotheses are appropriate for testing this claim about the slope of the population regression line predicting $y$ from $x$?
4. A gym claims that the mean weight loss after an 8-week program is 6 lb. A statistician tests $H_0: \mu=6$ vs. $H_a: \mu\neq6$ at $\alpha=0.05$. The p-value is 0.31, so the statistician fails to reject $H_0$ and reports no convincing evidence that the mean weight loss differs from 6 lb. In reality, the true mean weight loss is $\mu=8$ lb. Which type of error was made?
5. A university is evaluating whether the proportion of first-year students who return for the second year is higher for students who participated in a summer bridge program than for those who did not. Of 180 bridge participants, 153 returned; of 200 non-participants, 158 returned. Which hypotheses are appropriate?
6. A fitness tracker company claims the mean number of steps per day for its users is $\mu=10{,}000$. A random sample of users yields a 92% confidence interval for $\mu$ of $(9{,}700,\ 10{,}300)$. Is the claim supported by the confidence interval?
7. A botanist studies whether the amount of fertilizer applied affects plant height. In an experiment, 40 plants are randomly assigned different fertilizer amounts, and the botanist records fertilizer in grams (explanatory variable $x$) and final height in centimeters (response variable $y$). A regression line is fit to predict height from fertilizer. The botanist's claim is that more fertilizer increases height, so the population slope is positive. Which hypotheses are appropriate for testing this claim about the slope?
8. A bookstore tracks $X$, the number of books sold in the first hour after opening on a randomly selected day. The distribution of $X$ has mean $\mu_X=27.5$ books and standard deviation $\sigma_X=6.2$ books. Which interpretation of the standard deviation is correct?
9. A game awards a random number of bonus points, $X$, each time it is played. The distribution of $X$ is discrete with mean $\mu_X=12$ points and standard deviation $\sigma_X=4$ points. Which interpretation of the standard deviation is correct?
10. For a binomial variable with fixed n, changing p from 0.25 to 0.75 will cause the variance to:
11. A car reviewer recorded data from $n=28$ vehicles on engine size ($x$, liters) and highway fuel efficiency ($y$, miles per gallon). A least-squares regression of mpg on engine size gave slope $b_1=-4.1$. The reviewer tested $H_0: \beta_1=0$ versus $H_a: \beta_1<0$ and obtained a p-value of $0.012$. Based on this completed slope test at $\alpha=0.05$, what conclusion is appropriate?
12. A university wants to test whether background music affects quiz performance. The explanatory variable is music condition (music vs. no music), and the response variable is quiz score out of 20. Students volunteer, and the researcher flips a coin for each student to assign the music condition during the quiz. Afterward, the researcher concludes that music causes higher quiz scores for all college students. Which statement best describes what is justified from this study design?
13. A city planner samples 50 commute distances (in miles) for workers who drive to downtown. A histogram of the distances shows most commutes between 2 and 12 miles, with frequencies decreasing steadily as distance increases, and a tail extending out to 40 miles. Which statement best describes the distribution?
14. A university dining hall recorded the entrée choice for a random sample of 180 lunches on a Tuesday (categorical variable). The bar chart shows counts: Pizza 46, Salad 39, Sandwich 51, Pasta 28, Stir-fry 16. Which statement is supported by the graph?
15. A poll compares the proportion of voters who favor Candidate R among Independents versus Democrats. A 95% confidence interval for the difference in proportions, defined as $p_I - p_D$, is $(0.01, 0.25)$. A commentator claims, "Independents have a higher proportion favoring Candidate R than Democrats." Is the claim supported by the confidence interval?
16. A school compares the mean number of minutes of homework completed per night for students using a planner app (Group A) versus students not using it (Group B). The researchers report a 95% confidence interval for $\mu_A-\mu_B$ of $(4.2,\ 12.8)$ minutes and claim that planner-app users complete more homework on average. Is the claim supported by the interval?
17. A basketball player takes 15 free throws during practice. Define a success as making a free throw. The player's long-run free-throw percentage is $0.78$, and each shot is considered independent of the others. Which values correctly model this situation with a binomial random variable $X$ = number of successes?
18. A city wants to estimate the mean time (in minutes) that all city bus riders wait at stops during weekday mornings. The transit office randomly selects 30 bus stops from a complete list of all stops in the city and posts an employee at each selected stop on a Tuesday from 7:00–9:00 a.m. to record wait times for every rider who arrives during that window. Which statement best describes the sample representativeness?
19. Before concluding that the flu shot helps protect against pneumonia, which question is most important to investigate from a statistical standpoint?
20. A bakery fills a randomly selected box with a small number of cookies as a promotional sample. Define a discrete random variable $C$ as the number of cookies in the box (1, 2, or 3). The probability distribution of $C$ is shown in a table. Which statement correctly interprets the random variable?

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