Practice Test 80 - AP Statistics

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

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1. A city compares mean commute time (minutes) for residents who take public transit versus those who drive. Two independent random samples produce a 95% confidence interval for $(\mu_{\text{transit}}-\mu_{\text{drive}})$ of $(2,\ 9)$ minutes. Which interpretation is correct?
2. A scatterplot of data for the price of a used car versus its age in years shows that as the age of the car increases, its price tends to decrease. How would the direction of this association be described?
3. The distribution of resting heart rates (beats per minute) for the population of adult runners in a club is approximately Normal with mean $\mu=60$ bpm and standard deviation $\sigma=8$ bpm. The marked value is $x=44$ bpm. Which statement about the marked value is correct?
4. A school district tests whether a new tutoring program changes the mean math score. They use $H_0: \mu=70$ vs. $H_a: \mu\neq 70$ with $\alpha=0.10$. The district rejects $H_0$ and concludes the program changes the mean score. In truth, the program has no effect and the population mean remains $\mu=70$. Which type of error was made?
5. A basketball player practices free throws until making the first shot. Assume each shot is independent and the probability of making any shot is $p$ each time. The player records the number of shots taken until the first made free throw. Why is a geometric model appropriate?
6. A city considers changing a traffic-light timing plan after a sample of 40 weekday mornings shows the average commute time on a major corridor decreased by 2.5 minutes with the new plan. The transportation director wants to implement the change citywide, but longer commutes could increase accident risk and delay emergency vehicles. Why is it important to consider potential error?
7. A manufacturer advertises that at least 95% of its light bulbs last 1,000 hours. A quality-control team randomly tests 200 bulbs and finds that 186 last at least 1,000 hours (so $\hat{p}=0.93$). Which hypotheses are appropriate for testing whether the advertisement is overly optimistic about the population proportion $p$ of all bulbs that last 1,000 hours?
8. A librarian studies whether the number of hours a student spends in the library per week ($x$) predicts the number of books the student checks out per month ($y$). The librarian believes that more library time leads to more checkouts in the population. Which hypotheses are appropriate for testing this claim about the regression slope?
9. A nutritionist wants to estimate the mean sodium content (in mg) of a certain brand of canned soup. She randomly selects 40 cans and measures sodium content. A 95% confidence interval for the population mean sodium content is $(820, 880)$ mg. Which interpretation is correct?
10. A streaming company randomly samples 100 users and estimates the mean number of hours streamed per week. A 99% confidence interval for the population mean is $(13.2, 15.1)$ hours. An executive claims the true mean is 14 hours. Is the claim supported by the confidence interval?
11. A conservationist studies whether the number of visitors to a park per day ($x$) predicts the amount of litter collected in pounds ($y$). The conservationist claims that more visitors leads to more litter in the population. Which hypotheses are appropriate for testing this claim about the slope in the regression of $y$ on $x$?
12. A streaming service claims that 50% of its subscribers watch at least one documentary each month. A random sample of 300 subscribers found that 142 watched at least one documentary last month. A one-sample $z$ test for a population proportion was conducted with $H_0: p=0.50$ and $H_a: p\ne 0.50$ at $\alpha=0.05$. The test gave a $p$-value of 0.327, so the analyst failed to reject $H_0$. Which conclusion is appropriate?
13. A city compares mean commute time (minutes) for residents who use public transit (T) versus those who drive (D). A 99% confidence interval for $\mu_T-\mu_D$ is $(2,\ 18)$. A resident claims that public transit has a shorter mean commute time than driving. Is the claim supported by the interval?
14. What was the actual weight of this 6-month-old dog?
15. A botanist models amount of fertilizer ($x$, in grams) and plant height after 4 weeks ($y$, in cm) using a least-squares regression line to predict height from fertilizer. A scatterplot with the fitted line is shown. Which statement about the regression line is correct?
16. A machine produces light bulbs, and a quality inspector counts the number of defective bulbs in a randomly selected box of 5 bulbs. Let the discrete random variable $X$ be the number of defective bulbs in the box. The probability distribution of $X$ is shown in a table. Which statement correctly interprets the random variable $X$?
17. A jar contains 40 red marbles and 60 blue marbles. A student draws exactly 25 marbles without replacement and defines a success as drawing a red marble (failure = blue). The student records the number of red marbles drawn. Does this meet binomial conditions?
18. A weather app issues a "rain likely" alert on some mornings. Let event $A$ be "it rains that afternoon," and event $B$ be "the app issued a 'rain likely' alert that morning." The alert is designed to occur more often on days when rain is actually more likely, so $A$ is more likely given $B$ than overall. How does knowing that $B$ occurred affect the likelihood of $A$?
19. A school collects data on age of a car (x, in years) and its resale value (y, in thousands of dollars) for 12 used cars. The scatterplot shows value dropping quickly for newer cars and then dropping more slowly as cars get older. Which feature suggests a linear model is not appropriate for predicting resale value from age?
20. A hospital states that the mean length of stay for patients undergoing a certain procedure is $\mu=3.5$ days. A researcher suspects the mean length of stay has decreased with a new protocol. A random sample of 22 patients is collected, and a one-sample $t$ test is conducted with $H_0:\mu=3.5$ versus $H_a:\mu<3.5$ at $\alpha=0.05$. The p-value is 0.049. What conclusion is appropriate?

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