Practice Test 11 - AP Statistics

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

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1. A nonprofit organization claims that more than $65\%$ of adults in a county have volunteered in the past year. A random sample of $n=220$ adults finds $132$ have volunteered (so $\hat{p}=0.60$). Which hypotheses are appropriate to test the nonprofit's claim?
2. A delivery company summarizes the number of packages delivered per route for 45 routes last Friday. The five-number summary is: minimum $18$, $Q_1=30$, median $41$, $Q_3=55$, maximum $60$. A boxplot is constructed from these statistics. Which feature is consistent with the summary statistics?
3. A spinner has four equal sections labeled 1, 2, 3, 4. A student spins 16 times and records: 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4. Under random spinning you would expect repeats and irregular order, not a perfect cycle repeated four times. Is the pattern consistent with random behavior?
4. A streaming service tracks the number of episodes a subscriber watches in a day. Let $X$ be the number of episodes watched by a randomly selected subscriber on a randomly selected day; $X$ is discrete. The distribution of $X$ has mean $\mu_X=1.8$ episodes and standard deviation $\sigma_X=1.1$ episodes. Which interpretation of the mean is correct?
5. An environmental engineer samples $n=40$ days and fits a least-squares regression line predicting daily electricity use ($y$, kWh) from daily high temperature ($x$, °F). The engineer claims that, in the population, hotter days lead to higher electricity use (positive slope). Which hypotheses are appropriate for testing this claim about the population slope?
6. A grocery chain wants to estimate the proportion of all its customers who use digital coupons. For one week, the chain recorded whether each customer used a digital coupon for every 20th customer who checked out between 5 p.m. and 8 p.m. at each store. In the resulting sample of 900 customers, 41% used a digital coupon. The chain concluded that "about 41% of all customers use digital coupons." Which statement explains whether the conclusion is valid?
7. A school compares the mean number of minutes of homework done per night by students in two different programs. A random sample of $n_1=40$ students from Program A and an independent random sample of $n_2=35$ students from Program B are taken. Let $\bar{x}_A-\bar{x}_B$ be the difference in sample means. Which statement is correct about the sampling distribution of $\bar{x}_A-\bar{x}_B$?
8. A survey suggests that 70% of adults drink coffee daily. A student repeatedly selects many random samples of $n=60$ adults and calculates $\hat p$ each time. Which statement about the sampling distribution is correct?
9. At a school fundraiser, each student who arrives draws one ticket from a box. Some tickets are marked "Prize," and some are marked "No prize." Students also either purchased a snack bundle earlier in the day or did not. Let event $A$ be "the student's ticket is a Prize," and event $B$ be "the student purchased a snack bundle." Because students who bought the bundle were more likely to receive a Prize ticket (organizers added extra Prize tickets to their box), $A$ and $B$ are not independent. How does knowing that $B$ occurred affect the likelihood of $A$?
10. Which of the following expressions correctly calculates the expected number of people who own a cat and have allergies, under the null hypothesis of no association?
11. A biologist models the mass of a fish ($y$, grams) from its length ($x$, cm) for fish measured between 10 cm and 30 cm. The least-squares regression line is $\hat{y}=-40+8x$. The purpose of the linear model is to summarize the linear association and predict typical mass for lengths within the observed range. Which interpretation of the model is correct?
12. A nutrition company surveys a random sample of 800 adults to estimate the proportion who take a daily multivitamin. The company wants to claim that at least 40% of all adults take a daily multivitamin. A 90% confidence interval for the population proportion is $(0.41, 0.46)$. Is the claim supported by the confidence interval?
13. A researcher wants to know whether pet ownership (Dog, Cat, Neither) is related to housing type (House, Apartment). One random sample of residents is surveyed, and each person reports both variables. The counts are shown. Which test is appropriate, and what are the correct hypotheses?
14. A teacher records whether a randomly selected student is absent on a particular day. Define a discrete random variable $A$ as the number of days absent for that student during a 5-day week (0 through 5). The probability distribution of $A$ is shown in a table. Which statement correctly interprets the random variable?
15. A manufacturer advertises that 10% of its lightbulbs are defective. A quality-control team randomly samples 200 bulbs and finds 30 defective. They run a one-sample proportion test at $\alpha=0.01$ with hypotheses $H_0: p=0.10$ and $H_a: p\ne 0.10$. The test yields a $p$-value of 0.006, so they rejected $H_0$. Which conclusion is appropriate?
16. A researcher records each student's weekly study time (hours) and their score on a unit test (points). The scatterplot shows a clear upward trend with moderate scatter around a roughly straight-line pattern. Which statement about correlation is correct?
17. An environmental club wants to estimate the average number of plastic bottles used per day by students at their school. The plan is to count bottles in the recycling bins located near the gym for five school days and divide by the number of days. The research question is: "What is the mean number of plastic bottles used per day by all students at this school?" Which aspect is most important to address before collecting data?
18. An airline studies whether the number of minutes a flight is delayed at departure ($x$) predicts the number of minutes it arrives late ($y$). The airline expects that larger departure delays lead to larger arrival delays in the population. Which hypotheses are appropriate for testing this expectation about the slope in the regression of $y$ on $x$?
19. A science class measured the length (in centimeters) of 32 leaves from the same type of plant, using a ruler to the nearest 0.5 cm. The dotplot below shows the distribution of leaf lengths. Which feature of the distribution is most evident?
20. A marketing firm wants to estimate the mean amount of money (in dollars) spent per week on streaming services by adults in a certain city. The firm takes a simple random sample of 80 adults and records each person's weekly spending. The firm wants a 90% confidence interval for the population mean spending. Which inference procedure is most appropriate?

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