Practice Test 5 - AP Statistics

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

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1. A hospital reports that 8% of patients are readmitted within 30 days. A researcher randomly samples 300 discharged patients and finds 18 readmitted. A one-sample proportion test at $\alpha=0.05$ was performed with $H_0: p=0.08$ versus $H_a: p\ne 0.08$. The test resulted in a $p$-value of 0.20, so the researcher failed to reject $H_0$. Which conclusion is appropriate?
2. A bank studies whether an account holder misses a payment in a given month (event $A$) and whether the account holder has enabled automatic payments (event $B$). The bank expects these events to be associated. How does knowing that $B$ occurred affect the likelihood of $A$?
3. A teacher compared the proportion of students who pass a quiz after two different review methods. In one class using Method A, 31 of 50 students passed; in another class using Method B, 28 of 55 students passed. A 95% confidence interval for $p_A - p_B$ is $(-0.05,\ 0.27)$. Which interpretation is correct?
4. A researcher plans to call households until 10 people agree to complete a short survey. Each call results in either agreement (success) or refusal (failure). The researcher records the total number of calls needed to get 10 agreements. Does this meet the binomial conditions for modeling the number of successes?
5. A marketing firm claims that 40% of consumers prefer Brand A over Brand B. To check the claim, a simple random sample of 150 consumers is surveyed; 48 prefer Brand A and 102 prefer Brand B. The firm wants to test whether the true preference proportion differs from 0.40. Which inference procedure is most appropriate?
6. A university dining services team is researching beverage choices among students who eat lunch on campus. A random sample of 150 students is asked to choose their most common lunch beverage (a categorical variable). The results are summarized below. Which statement is supported by the data?

   Lunch beverage	Frequency	Relative frequency
   Water	63	0.420
   Soda	36	0.240
   Coffee/Tea	30	0.200
   Juice	21	0.140

7. A public health researcher wants to estimate the difference in the proportion of adults who received a flu shot this year between Urban County and Rural County. Independent random samples are taken: 400 adults from Urban County and 350 adults from Rural County, and each adult is classified as vaccinated or not. The researcher wants a 95% confidence interval for $p_{Urban}-p_{Rural}$. Which inference procedure is most appropriate?
8. What are the mean and standard deviation of X?
9. A hospital compares two treatments using a randomized study and finds Treatment A has a higher recovery rate in the sample. The hospital plans to switch all patients to Treatment A, but switching could increase costs and, if the conclusion is wrong, harm patients. Why is it important to consider potential error when using the study's result to choose a treatment?
10. A physics student measured the stopping distance (y) of a toy car versus its initial speed (x). The scatterplot shows stopping distance increases slowly at low speeds but much more rapidly at higher speeds. Which feature suggests that a linear model may not be appropriate?
11. In a study of 50 randomly selected customers at a coffee shop, a manager recorded the number of minutes each customer waited from ordering to receiving a drink during the morning rush. The dotplot shows the distribution of wait times (in minutes). Which feature of the distribution is most evident?
12. A health organization takes a simple random sample of 800 adults in a state and asks whether they received a flu shot this season. In the sample, 456 adults report receiving a flu shot. A 92% confidence interval for the true proportion $p$ of all adults in the state who received a flu shot is $(0.54,\ 0.60)$. Which interpretation is correct?
13. A streaming service reports that 25% of its subscribers watch documentaries each week. Suppose many random samples of $n=120$ subscribers are taken and $\hat p$ is recorded. Which statement about the sampling distribution is correct?
14. A real estate analyst fits a regression model predicting house sale price ($y$) from square footage ($x$). The analyst claims that each additional square foot increases mean sale price by more than $150$ dollars (slope $>150$). A 99% confidence interval for the slope is $(120,\ 190)$ dollars per square foot. Is the claim supported by the confidence interval?
15. A school surveyed students about grade level (9th or 12th) and whether they participate in an after-school club (Yes/No). Use the two-way table to decide which comparison is appropriate for describing the relationship between grade level and club participation using conditional distributions. Which comparison is appropriate?
16. A university claims the population mean GPA of incoming first-year students is $\mu=3.20$. From a random sample of incoming students, a 98% confidence interval for $\mu$ is reported as $(3.18,\ 3.22)$. Is the claim supported by the CI?
17. A music streaming service analyzes the number of songs users listen to in a day. The population distribution is not normal: it is highly right-skewed, with many users listening to few songs and a small group listening to many. A random sample of $n=55$ users is taken, and the sample mean number of songs is calculated. Why is the sampling distribution of $\bar{x}$ approximately normal?
18. A city official claims the mean one-way commute time for residents is $\mu=28$ minutes. A random sample of residents is taken, and a 95% confidence interval for $\mu$ is $(29.1,\ 32.4)$ minutes. Is the claim supported by the confidence interval?
19. A teacher summarized scores (out of 100) on a quiz for 95 students. The statistics were: mean $=78$, median $=82$, SD $=10$, five-number summary $(35,\ 72,\ 82,\ 88,\ 96)$, and IQR $=16$. Which interpretation is correct?
20. A biologist measures the length of a lizard (cm) and its sprint speed (m/s). The scatterplot shows an increasing pattern that curves upward (not well-approximated by a straight line). Which statement about correlation is correct?

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