Practice Test 8 - AP Statistics

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

Start practice test

1. A marketing team randomly sampled customers from two age groups (18–34 and 35+) and recorded whether each customer prefers Brand X, Brand Y, or Brand Z. The two-way table is shown. A chi-square test of homogeneity comparing the distribution of brand preference across the two age groups gave $p$-value $=0.41$. What conclusion is appropriate at the 5% significance level?
2. A wildlife camera is set to take one photo every minute and classify each as "Deer" or "No Deer." Over 120 minutes, the results appear in clusters: long blocks of "No Deer" with occasional bursts where "Deer" appears repeatedly for several minutes in a row. If deer activity is influenced by animals moving through the area, you might expect dependence (clumping) rather than independent random minute-to-minute outcomes. Is the observed clustering consistent with random behavior (independent trials with a constant probability of deer each minute)?
3. A manufacturer claims that at least 90% of customers are satisfied with a product. A random sample of customers yields an 80% confidence interval for the true proportion $p$ satisfied: $(0.88,\ 0.93)$. Is the claim supported by the confidence interval?
4. A researcher wants to know whether the proportion of commuters who use public transportation is different for people who work day shift versus night shift. An independent random sample of 110 day-shift workers finds 28 who use public transportation; an independent random sample of 90 night-shift workers finds 34 who use public transportation. Which inference procedure is most appropriate?
5. A fitness researcher recorded the number of minutes of moderate-to-vigorous exercise per week for a random sample of 80 adults in a city. The summary statistics were: mean $=154$ min, median $=140$ min, SD $=60$ min, five-number summary $(20,\ 90,\ 140,\ 200,\ 360)$, and IQR $=110$ min. Which interpretation is correct?
6. A candy company claims that a bag of its assorted candies contains 20% red, 20% blue, 20% green, 20% yellow, and 20% orange candies. A student counts the colors in a randomly selected bag containing 100 candies; results are shown in a table. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the company's claim?
7. A school wants to know whether students' preferred study location is associated with grade level. A random sample of students is taken, and each student reports their preferred location (Home, Library, or Study Hall). The results are summarized below. A chi-square test of independence is performed and yields $p=0.018$. What conclusion is appropriate at the $\alpha=0.05$ level? Two-way table (counts):

   Grade level	Home	Library	Study Hall
   9th	30	18	12
   10th	22	25	13
   11th	18	28	14
   12th	20	15	25

8. A streaming service randomly sampled 800 subscribers and found that 520 watched at least one documentary in the last month. A 95% confidence interval for the true proportion $p$ of all subscribers who watched at least one documentary in the last month is $(0.62,\ 0.68)$. Which interpretation is correct?
9. A restaurant owner wants to estimate the mean amount (in dollars) that customers spend per visit. A random sample of 80 customer receipts from the past month was selected, and a 90% confidence interval for the population mean spending was computed as $(12.40, 14.10)$. Which interpretation is correct?
10. A climatologist studies whether atmospheric CO$_2$ concentration in ppm ($x$) predicts average global temperature anomaly in °C ($y$). The climatologist claims that higher CO$_2$ is associated with higher temperature anomaly in the population. Which hypotheses are appropriate for testing this claim about the slope in the regression of $y$ on $x$?
11. A poll of 400 adults recorded whether they support a policy and whether they are under 30 or 30 and over. Assuming independence, which expression calculates the expected count for the Under 30 & Support cell?
12. A public health report claims the mean number of hours adults sleep per night is $\mu=7.0$ hours. Researchers take a random sample and construct a 95% confidence interval for $\mu$ of $(6.8,\ 7.2)$ hours. Is the claim supported by the confidence interval?
13. A researcher studies whether the number of hours spent volunteering per month ($x$) predicts a community engagement score ($y$). The researcher claims that more volunteering is associated with higher engagement in the population. Which hypotheses are appropriate for testing this claim about the slope of the population regression line predicting $y$ from $x$?
14. A restaurant chain claims that the proportion of customers who would recommend the restaurant is $0.85$. A random sample of $n=100$ customers finds $80$ would recommend it (sample proportion $\hat{p}=0.800$). Which hypotheses are appropriate to test whether the true proportion is different from $0.85$?
15. A lab runs 10 independent bacteria cultures and records whether each culture shows antibiotic resistance. A success is "resistant," and exactly 10 cultures are tested under identical conditions. Does this meet binomial conditions?
16. A restaurant chain wants to estimate the proportion of all customers who were satisfied with their visit. Each receipt includes a QR code linking to a satisfaction survey, and customers who complete it are entered into a drawing for a $50 gift card. The chain reports the satisfaction rate from completed surveys. Which issue most threatens the validity of this estimate?
17. A streaming service advertises that fewer than 25% of its subscribers cancel within the first month. From a random sample of 500 new subscribers, a 99% confidence interval for the true cancellation proportion is $(0.20, 0.24)$. Is the claim supported by the confidence interval?
18. A farmer compares mean weight (kg) of pumpkins grown with Fertilizer 1 versus Fertilizer 2. From independent random samples, a 95% confidence interval for $(\mu_1-\mu_2)$ is $(-0.8,\ 1.6)$. Which interpretation is correct?
19. A statistician would caution against this conclusion primarily because...
20. A candidate claims that exactly 40% of voters in the district currently support them. A random sample of voters yields a 95% confidence interval for the population proportion who support the candidate of $(0.35, 0.39)$. Is the claim supported by the confidence interval?

Practice tests