Practice Test 77 - AP Statistics

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

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1. Each count in a categorical table is doubled. Which graph stays exactly the same?
2. A teacher demonstrates "random seating" by assigning each student to a seat number from 1 to 30 using slips of paper. Over several days, students notice Seat 1 is assigned every day to someone whose last name begins with A–F, and Seat 30 is assigned every day to someone whose last name begins with T–Z. Under random assignment, seat numbers should not consistently be associated with last-name groups. Is the pattern consistent with random behavior?
3. The weights of packages shipped from a warehouse are approximately Normal with mean $\mu=12$ lb and standard deviation $\sigma=1.5$ lb. Without calculating probabilities, which comparison is supported by symmetry?
4. A student tracks whether they arrive to class early (E) or not (L) over 25 days. The record is: E L E L E L E L E L E L E L E L E L E L E L E L E. Is the pattern consistent with random behavior?
5. A city transportation office claims that weekday subway riders use entry gates in these proportions: North 0.35, South 0.25, East 0.20, West 0.20. A random sample of $n=500$ riders is recorded with counts shown below. A chi-square goodness-of-fit test gives p-value = 0.27. What conclusion is appropriate at the $\alpha=0.05$ level? Observed/Expected counts (with p-value):

   Gate	Observed	Expected
   North	170	175
   South	118	125
   East	106	100
   West	106	100

   p-value = 0.27
6. A wildlife biologist claims that the proportion of a certain frog species in a wetland that carries a parasite is no more than $0.10$. The biologist captures a random sample of $n=300$ frogs and finds $39$ with the parasite (sample proportion $\hat{p}=0.130$). Which hypotheses are appropriate to test the biologist's claim?
7. A factory measures two independent random variables for a batch: $X$, the weight (in grams) of a packaged snack, with $\mu_X=55$ and $\sigma_X=2$, and $Y$, the weight (in grams) of the box it is placed in, with $\mu_Y=15$ and $\sigma_Y=1$. Let $S=X+Y$ be the total shipping weight. Which statement about $S$ is correct?
8. A nutrition researcher studies the sodium content (in milligrams) of individual servings of a packaged soup. The population has mean $\mu=910$ mg and standard deviation $\sigma=120$ mg. The researcher repeatedly takes simple random samples of size $n=9$ servings and calculates the sample mean $\bar{x}$. Which statement about the sampling distribution of $\bar{x}$ is correct?
9. A streaming service takes a simple random sample of 600 subscribers and asks whether they plan to cancel in the next month. In the sample, 78 say they plan to cancel. A 90% confidence interval for the true proportion $p$ of all subscribers who plan to cancel in the next month is $(0.11,\ 0.15)$. Which interpretation is correct?
10. A coin is advertised as fair, so the probability of heads is 0.50. A student flips the coin 10 times and gets 8 heads. The student wonders whether 8 heads out of 10 is surprising due to random chance with such a small number of flips if the coin is actually fair. Is the result unexpected?
11. A bookstore manager claims the mean amount spent per customer visit is $\mu=22$ dollars. A random sample of customers is used to compute an 88% confidence interval for the population mean spending per visit: $(19.5,\ 21.8)$ dollars. Is the claim supported by the confidence interval?
12. A shipping company measures the delivery times (in hours) for a random sample of 75 packages sent by standard service between two cities. The distribution is roughly bell-shaped with only mild skew and no unusual gaps. Why is a normal model reasonable for analyzing delivery times in this situation?
13. A manufacturer wants to test whether the mean fill volume of a drink bottle is 500 mL. A simple random sample of 36 bottles from today's production line is selected, and each bottle's fill volume (mL, quantitative) is measured. The population standard deviation is not known. Which inference procedure is most appropriate to test $H_0: \mu=500$ vs. $H_a: \mu\ne 500$?
14. A call center models the probability a customer call is resolved on the first attempt as 0.4, independently across calls. A supervisor wants to estimate the probability that in the next 6 calls, exactly 3 are resolved on the first attempt. She simulates 10,000 trials; in each trial she generates 6 random digits (0–9), lets 0–3 represent "resolved" and 4–9 represent "not resolved," and counts how often exactly 3 resolved. The simulation produced 2768 trials with exactly 3 resolved. Which interpretation of the simulation results is correct?
15. A hospital administrator models patient satisfaction score ($y$) from average waiting time in minutes ($x$). The administrator claims that each additional minute of waiting decreases mean satisfaction by at most 0.3 points (slope $\ge -0.3$). A 95% confidence interval for the slope is $(-0.55,\ -0.10)$ satisfaction points per minute. Is the claim supported by the confidence interval?
16. A teacher wanted to test whether providing written feedback on practice essays improves scores on a final in-class essay. The teacher had two existing class sections of the same course (Section 1 and Section 2). Section 1 received written feedback on each practice essay for 4 weeks, while Section 2 received only a completion checkmark. At the end, Section 1 had a higher mean final essay score. Students were not randomly assigned to sections, and the teacher did not randomly assign the feedback method. Which conclusion is justified based on the design of this study?
17. A tech company claims that 55% of users prefer the new app interface. A random sample of 400 users found that 204 prefer the new interface. A one-sample $z$ test for a population proportion was conducted with $H_0: p=0.55$ versus $H_a: p<0.55$ at significance level $\alpha=0.05$. The test produced a $p$-value of 0.009, so the null hypothesis was rejected. Which conclusion is appropriate?
18. A statewide university system wants to estimate the proportion of all enrolled undergraduates who support a proposed tuition increase. An email survey link is sent to every undergraduate, but only about 12% of students respond after two reminder emails. The results are reported as the systemwide estimate. Which issue most threatens the validity of the estimate?
19. Based on this information, which is the most appropriate statistical statement about the variables 'daily rainfall' and 'number of accidents'?
20. A basketball player makes a free throw with probability 0.7 on each attempt. A coach wants to estimate the probability the player makes at least 4 out of 5 free throws. The coach simulates 8,000 sets of 5 shots by generating random two-digit numbers 00–99 for each shot and letting 00–69 represent "make." The simulation produced 4,639 sets with at least 4 makes. Which interpretation of the simulation results is correct?

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