Practice Test 53 - AP Statistics

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

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1. A real estate analyst randomly samples 35 homes in a region and records home size ($x$, square feet) and selling price ($y$, thousands of dollars). A least-squares regression line predicts price from size. A 98% confidence interval for the true slope is $(0.08,\ 0.14)$ thousand dollars per square foot. Which interpretation is correct?
2. A basketball player shoots free throws until making 10 shots. A success is a made free throw and a failure is a missed free throw. The coach wants to use a binomial model for the number of made shots. Does this meet binomial conditions?
3. A researcher compares mean resting heart rate (beats per minute) between runners and non-runners. Independent random samples were taken from each group. A two-sample $t$ test was conducted for $H_0: \mu_R-\mu_N=0$ versus $H_a: \mu_R-\mu_N<0$. The p-value was 0.001. At $\alpha=0.05$, what conclusion is appropriate?
4. A public health researcher tests whether the proportion of adults in a county who have received a flu shot is greater than 50%. In a random sample of 300 adults, 171 reported receiving a flu shot. A one-proportion $z$ test was conducted for $H_0: p=0.50$ versus $H_a: p>0.50$ at $\alpha=0.05$. The $p$-value was 0.006, so the researcher rejected $H_0$. Which conclusion is appropriate?
5. A movie theater tracks the number of times a randomly selected customer refills a drink during a movie. Let $X$ be the number of refills. The probability distribution of $X$ is shown in a table. Which statement correctly interprets the random variable $X$?
6. A realtor tracked the selling prices (in thousands of dollars) of 50 homes in a neighborhood. The summary statistics were: mean $= 365$, median $= 340$, standard deviation $= 110$, five-number summary $(180, 260, 340, 420, 820)$, and IQR $= 160$. Which interpretation is correct?
7. A physics class records the angle of a ramp (x, in degrees) and the time for a cart to travel a fixed distance (y, in seconds). The scatterplot shows time decreasing rapidly at small angles and then decreasing more slowly at larger angles. Which feature suggests a linear model is not appropriate?
8. A researcher studying the weights of a species of adult bird finds two distinct subgroups within the data: one for males and one for females, where males are typically heavier than females. Which of the following features would most likely be observed in the overall distribution of weights for the combined group of birds?
9. A city wants to estimate the proportion of households that support a proposed recycling fee. A simple random sample of 500 households is contacted, and each household responds either "support" or "do not support." The parameter of interest is the population proportion who support the fee. Which inference procedure is most appropriate?
10. A hospital wants to estimate the proportion of patients who would recommend the emergency department to a friend. A simple random sample of 250 recent patients is contacted; 172 say "Yes" and 78 say "No." Which inference procedure is most appropriate to estimate the true recommendation proportion with a confidence interval?
11. An ecologist models the number of bird species observed at a site from the size of the site (acres). The ecologist claims that larger sites are associated with more species on average. A 95% confidence interval for the slope is $(0.02,\,0.11)$ species per acre. Is the claim supported by the confidence interval?
12. A librarian recorded the number of books checked out by each of 45 patrons during a particular week, using the library's checkout database. The dotplot shows the distribution of books checked out. Which feature of the distribution is most evident?
13. A nutrition blogger claims that people who eat breakfast have lower body mass index (BMI) than people who skip breakfast. To investigate, the blogger surveyed 500 followers on social media who chose to respond, asking whether they usually eat breakfast and their current BMI. Respondents who reported eating breakfast had lower average BMI. Which conclusion is justified based on the design of this study?
14. A company wants to estimate the average satisfaction rating (1–10) among all customers who made a purchase in the last month. They randomly select 800 customers from their database and call them. Of those selected, 430 answer the phone and complete the survey; the company reports the mean rating from the 430 responses. Which issue most threatens the validity of generalizing to all customers?
15. A wildlife agency reports that 25% of households in a region regularly put out bird feeders. A researcher suspects the true proportion is less than 25%. In a random sample of 160 households, 32 report regularly putting out bird feeders ($\hat{p}=0.20$). Which hypotheses are appropriate for testing the researcher's suspicion?
16. A teacher compares mean quiz scores for students who used flashcards versus students who did not. The claim is that flashcard users score higher on average. A 95% confidence interval for $(\mu_{\text{flashcards}}-\mu_{\text{no flashcards}})$ is $(-1.2,\ 8.4)$ points. Is the claim supported by the confidence interval?
17. A dermatologist wants to compare two acne creams (Cream A vs. Cream B). Each patient has acne on both the left and right side of their face, and the dermatologist believes acne severity varies a lot from person to person. Each patient can safely use both creams at the same time, one on each side, for 6 weeks, and the response is reduction in acne lesions per side. Which experimental design is most appropriate?
18. A medical clinic compares mean systolic blood pressure (mmHg) between patients who follow a low-sodium diet and patients who do not. A random sample of $n=40$ low-sodium patients had mean $\bar{x}=126.3$ mmHg, and a random sample of $n=42$ patients with no diet change had mean $\bar{x}=131.7$ mmHg. The claim is that the low-sodium diet results in a lower population mean systolic blood pressure. Which hypotheses are appropriate?
19. A distribution of data is approximately symmetric and unimodal with no significant outliers. Which statement accurately describes the expected relationship between the mean and median?
20. A city compares mean commute time (minutes) for residents who use public transit versus those who drive. From independent random samples, a 90% confidence interval for $(\mu_{\text{transit}}-\mu_{\text{drive}})$ is $(5,\ 18)$. Which interpretation is correct?

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