Practice Test 56 - AP Statistics

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

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1. A company wants to estimate the mean number of hours per week its 3,000 employees work from home. The population is all employees. The company divides employees into departments (Engineering, Sales, HR, Support) and then randomly selects 50 employees from each department using a random number generator, for a total of 200 employees surveyed. Which statement best describes the sample representativeness?
2. A grocery store tests whether a new checkout layout reduces mean customer wait time. A random sample of $n=25$ customers in the new layout had mean wait time $\bar{x}=3.9$ minutes, and a random sample of $n=27$ customers in the old layout had mean wait time $\bar{x}=4.6$ minutes. The store's claim is that the new layout has a lower population mean wait time than the old layout. Which hypotheses are appropriate?
3. Which assumption for regression inference is most likely violated according to this plot?
4. A commuter records $X$, the number of red lights encountered on the drive to work. The distribution of $X$ has mean $\mu_X=5.8$ and standard deviation $\sigma_X=1.9$. Which interpretation of the mean is correct?
5. A city reports that 6% of parking meters are broken at any given time. Many random samples of $n=300$ meters are inspected and $\hat p$ is recorded each time. Which statement about the sampling distribution is correct?
6. Two brands of batteries are tested for how long they last (hours) in the same device. The results are summarized below. Which comparison is supported?

   Statistic	Brand X	Brand Y
   Mean	9.8	10.1
   Median	10.2	9.9
   Shape	left-skewed	right-skewed
   IQR	1.4	1.4

7. A bottling plant targets an average fill volume of $\mu=2.00$ liters. A random sample of 50 bottles is measured, and a one-sample $t$ test is carried out with $H_0:\mu=2.00$ and $H_a:\mu\neq 2.00$ at $\alpha=0.05$. The p-value is 0.62. What conclusion is appropriate?
8. A researcher compares mean systolic blood pressure for adults who follow Diet A and Diet B. The claim is that Diet A leads to a lower mean systolic blood pressure than Diet B. A 95% confidence interval for $(\mu_{A}-\mu_{B})$ is $(-6.2,\ 1.5)$ mmHg. Is the claim supported by the confidence interval?
9. A bookstore owner claims that the distribution of customers' preferred format is 60% print, 25% e-book, and 15% audiobook. A random sample of 160 customers is surveyed; results are shown in a table. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the owner's claim?
10. A lab claims that 11% of test results are inconclusive. Many random samples of $n=80$ tests are taken and $\hat p$ is computed each time. Which statement about the sampling distribution is correct?
11. A manager wants to estimate the mean time (in minutes) customers spend waiting in line at a coffee shop during the morning rush. A random sample of 25 customers is observed, and a 90% confidence interval for the population mean waiting time is $(3.2, 4.6)$ minutes. Which interpretation is correct?
12. A school compares the proportion of students who pass an Algebra end-of-course exam after using two different review programs. In a random sample, 78 of 120 students using Program A passed, and 64 of 120 students using Program B passed. A two-proportion $z$ test was performed for $H_0: p_A-p_B=0$ versus $H_a: p_A-p_B>0$, and the p-value was $0.018$. Using $\alpha=0.05$, what conclusion is appropriate?
13. A political analyst claims that in a certain county, party registration is 45% A, 40% B, and 15% C. A random sample of 200 registered voters produced the counts below. A chi-square goodness-of-fit test at $\alpha=0.05$ gives $p$-value $=0.07$. What conclusion is appropriate?
14. A real estate agent summarizes the sale prices (in thousands of dollars) for 55 homes sold in one neighborhood last year. The five-number summary is: min $=190$, $Q_1=240$, median $=310$, $Q_3=400$, max $=650$. A modified boxplot (1.5·IQR rule) is created. Which feature is consistent with the summary statistics?
15. A school cafeteria manager wants to compare three different menu layouts (A, B, C) to see which leads to the highest average number of fruit servings selected per student at lunch. Fruit selection differs a lot by grade level (9th, 10th, 11th, 12th), and the manager can implement only one layout per lunch period. Which experimental design is most appropriate to estimate the effect of layout while accounting for grade level?
16. A hospital compares mean length of stay (days) for patients receiving a new discharge protocol vs the old protocol. From two independent random samples, a 97% confidence interval for $(\mu_{new}-\mu_{old})$ is $(0.2, 1.4)$. Which interpretation is correct?
17. A medical test returns a false positive 3% of the time for healthy patients. A clinic wants to estimate the probability that, among 5 healthy patients tested independently, at least one receives a false positive. They simulate 25,000 groups of 5 by generating random integers 1–100 for each patient and letting 1–3 represent "false positive." The simulation found 3,675 groups with at least one false positive. Which interpretation of the simulation results is correct?
18. A fitness coach records resting heart rate ($y$, beats per minute) and weekly aerobic exercise time ($x$, minutes) for 14 clients. A least-squares regression line is fit to predict resting heart rate from exercise time: $\hat{y}=78.4-0.06x$. The purpose of this linear model is to describe the association and predict typical resting heart rate for clients with exercise times similar to those observed. Which interpretation of the model is correct?
19. A coffee shop claims that orders are distributed across 5 drink types as follows: Latte 28%, Cappuccino 22%, Drip 30%, Tea 15%, Other 5%. A random sample of 200 orders produced the counts below. A chi-square goodness-of-fit test at $\alpha=0.05$ reports $p$-value $=0.52$. What conclusion is appropriate?
20. A teacher wants to estimate the proportion of students in the entire school who prefer digital textbooks over printed textbooks. The plan is to survey the teacher's own classes because those students are easy to access. The research question is: "What proportion of all students in the school prefer digital textbooks?" Which aspect is most important to address before collecting data?

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