Practice Test 47 - AP Statistics

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

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1. A public library is evaluating how adult patrons prefer to access books. From the population of adult patrons who used the library this month, the library selects a random sample of 80 patrons and records each patron's preferred format (a categorical variable). The distribution is shown below. Which statement is supported by the data?

   Preferred book format	Frequency	Relative frequency
   Print	44	0.550
   E-book	20	0.250
   Audiobook	12	0.150
   Other	4	0.050

2. In a certain city, the distribution of adult systolic blood pressure (in mmHg) is approximately Normal for the population of all adults. The mean is $\mu=120$ with standard deviation $\sigma=15$. A value of 90 mmHg is marked on the normal curve. Which statement about the marked value is correct?
3. A game developer claims players choose among 3 character classes in the population with proportions 0.50 Warrior, 0.30 Mage, 0.20 Rogue. In a random sample of 250 new players, the observed counts are Warrior 132, Mage 63, Rogue 55. A chi-square goodness-of-fit test is performed and yields $p$-value = 0.072. Expected counts under $H_0$ are Warrior 125, Mage 75, Rogue 50. What conclusion is appropriate at $\alpha=0.10$?​
4. A university wants to check whether the proportion of students who prefer online sections is less than 40%. In a random sample of 250 students, 112 said they prefer online sections. A one-sample $z$ test for a population proportion was conducted with $H_0: p=0.40$ and $H_a: p<0.40$ at $\alpha=0.05$. The $p$-value was 0.214, so the university failed to reject $H_0$. Which conclusion is appropriate?
5. A school district wants to estimate the mean salary of all teachers in the district. A random sample of 60 teachers is taken, and a 95% confidence interval for the population mean salary is $(\$54{,}200, \$58{,}900)$. Which interpretation is correct?
6. A biology student measured the amount of fertilizer applied to $n=25$ plants (grams, $x$) and the plants' growth after 4 weeks (centimeters, $y$). The least-squares regression of growth on fertilizer gave slope $b_1=0.31$. The student tested $H_0: \beta_1=0$ versus $H_a: \beta_1>0$ at the 0.05 level and reported a p-value of $0.41$. Based on this completed slope test, what conclusion is appropriate?
7. A gym claims the mean weight loss for members after a 12-week program is $\mu=10$ lb. A random sample of participants is used to compute an 80% confidence interval for $\mu$ of $(7.5,\ 9.8)$ lb. Is the claim supported by the confidence interval?
8. A coach claims the mean height of players on a team is $\mu=72$ inches. A random sample of players gives a 98% confidence interval for $\mu$ of $(72.4,\,75.1)$. Is the claim supported by the confidence interval?
9. A coffee shop tracks the number of pastries a randomly selected customer buys during a visit. Let $X$ be the number of pastries purchased. The probability distribution of $X$ is given in the table. Which statement correctly interprets the random variable $X$?
10. A streaming service summarized the length (in minutes) of 90 movies watched by a sample of subscribers last month. The summaries were: mean $=104.0$, median $=101.0$, SD $=18.5$, $Q_1=92.0$, $Q_3=112.0$, minimum $=70$, maximum $=165$ (five-number summary: $70, 92, 101, 112, 165$). Which interpretation is correct?
11. A scatterplot of the number of years of education versus annual income for a random sample of adults shows a positive association. What does the phrase "positive association" imply in this context?
12. A researcher is studying whether background music affects proofreading accuracy. Each participant can complete two comparable proofreading passages in one session, but people vary widely in baseline proofreading skill. The researcher wants to compare Silence vs Instrumental Music and can randomize the order in which each participant experiences the two conditions. Which experimental design is most appropriate?
13. A geologist studies whether the depth of an earthquake in km ($x$) predicts the amount of surface damage in dollars ($y$). The geologist believes that deeper earthquakes tend to cause less surface damage in the population. Which hypotheses are appropriate for testing this claim about the slope in the regression of $y$ on $x$?
14. A student wants to test if a coin is biased towards landing on heads. The student flips the coin 40 times. Which of the following is a required condition to perform a valid one-sample z-test for the proportion of heads?
15. A wildlife biologist expects that a certain lake's fish population is about 50% female. The biologist catches a random sample of 12 fish and finds 10 are female. The expected behavior is that the sample proportion should be near 50%, but the observed outcome is about 83% female. Is this result unexpected, given the variability that can occur with random samples of size 12?
16. A public health researcher wants to compare smoking status across three regions of a state. Independent random samples of adults were taken from each region, and each adult was classified as a current smoker, former smoker, or never smoker. A chi-square test of homogeneity was conducted at $\alpha=0.05$. The observed counts and p-value are shown. What conclusion is appropriate?
17. A beverage company wants to test whether adding a citrus flavoring changes how sweet a drink is perceived. The explanatory variable is flavoring (citrus vs. none), and the response variable is the sweetness rating on a 1–9 scale. The company recruits 40 employees and randomly assigns 20 to taste the citrus version and 20 to taste the plain version. Each participant rates sweetness immediately after tasting. Which change would best reduce bias due to participants' expectations and improve the experimental design?
18. A city transportation office wants to know whether commute mode is related to commute time. For each of 150 workers leaving downtown at 5 p.m., an observer records the worker's commute mode (car, bus, bike, walk) and the number of minutes until the worker arrives home (self-reported the next day). The observational units are the workers. Which classification is correct?
19. A school compares mean nightly sleep for students who participate in a mindfulness program (M) versus those who do not (N). The researchers report a 95% confidence interval for the difference in population means, $\mu_M-\mu_N$, as $(0.2,\ 1.1)$ hours. A student claims: "Students in the mindfulness program sleep more on average than students not in the program." Is the claim supported by the confidence interval?
20. A researcher surveys a random sample of 300 adults and records two categorical variables: primary news source (TV, online, print) and political affiliation (Democrat, Republican, Independent). The researcher wants to know whether news source and political affiliation are associated in the population. Which inference procedure is most appropriate?

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