Practice Test 79 - AP Statistics

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

Start practice test

1. A college admissions office reviews applicants and records whether an applicant is admitted (event $A$) and whether the applicant applied by the early deadline (event $B$). The office notes that early applicants can differ from regular applicants in preparation and selectivity. How does knowing that $B$ occurred affect the likelihood that $A$ occurred?
2. A city wants to estimate the proportion of households that support a new recycling fee. The city has a list of all residential addresses and uses a random number generator to select 600 addresses to mail a survey. Only 210 households return the survey, and the city reports results using only those 210 responses. Which statement best describes the sample representativeness?
3. What is the expected number of patients for whom the drug is NOT effective, and what is the standard deviation of the number of patients for whom the drug is NOT effective?
4. A hospital administrator claims the mean waiting time in the emergency room is $\mu=38$ minutes. A random sample of patients yields a 97% confidence interval for the population mean waiting time of $(33\text{ min},\ 37\text{ min})$. Is the claim supported by the confidence interval?
5. For the population of fill amounts from a juice bottling machine, the fill volume is approximately Normal with mean $\mu=500$ mL and standard deviation $\sigma=10$ mL. The marked interval is from $490$ mL to $510$ mL. Which statement about the marked interval is correct?
6. A researcher summarized the reaction times (in milliseconds) of 45 participants completing a task. The five-number summary is: min $=210$, $Q_1=245$, median $=260$, $Q_3=290$, max $=410$. A boxplot is drawn based on these values. Which feature is consistent with the summary statistics?
7. A sports analyst compares the proportion of free throws made by players using two different training routines. Routine A: 150 made out of 200 attempts; Routine B: 138 made out of 200 attempts. A 95% confidence interval for $p_A-p_B$ is $(0.01,\ 0.13)$. The analyst claims Routine A leads to a higher free-throw success rate than Routine B. Is the claim supported by the confidence interval?
8. A retailer studies whether the number of items displayed at the front of a store ($x$) predicts daily impulse purchases ($y$). The retailer believes that more items displayed increases impulse purchases in the population. Which hypotheses are appropriate for testing this claim about the population regression slope?
9. A county wants to estimate the mean commute time for all employed adults living in the county. A researcher stands outside the county courthouse from 8:00–9:00 a.m. on a Monday and asks 150 people entering the building how long their commute was that day. No random selection is used. Which statement best describes the sample representativeness?
10. A counselor collected data on 10 students: number of absences in a semester ($x$) and final course percentage ($y$). Absences ranged from 0 to 12. A least-squares regression line to predict final percentage from absences is $\hat{y}=93-2.4x.$ The purpose of this linear model is to summarize the linear association and predict typical final percentages for students with absence counts within the observed range. Which interpretation of the model is correct?
11. A researcher compared mean reaction times (milliseconds) for two independent groups: participants who drank coffee (C) and participants who drank water (W). A 90% confidence interval for $\mu_C-\mu_W$ is $( -12,\ 30)$. Which interpretation is correct?
12. A university claims that more than 50% of applicants submit their application before the priority deadline. From a random sample of applicants, a 92% confidence interval for the population proportion who submit before the deadline is $(0.51, 0.59)$. Is the claim supported by the confidence interval?
13. A park ranger recorded the lengths (in inches) of 45 fish caught in a lake during one weekend. The five-number summary was: min $=6$, $Q_1=9$, median $=11$, $Q_3=14$, max $=20$. A boxplot is made. Which feature is consistent with the summary statistics?
14. A researcher surveys 40 randomly selected adults and asks whether each adult has a driver's license. A success is "has a license," and the researcher records the number of successes in the 40 responses. Does this meet binomial conditions to model the count of successes?
15. A school district tests whether a new tutoring program changes the mean math score from the historical mean of 75. The hypotheses are $H_0: \mu = 75$ and $H_a: \mu \ne 75$. At $\alpha = 0.01$, the district rejects $H_0$. However, in the full population, the true mean score with the program is still $\mu = 75$. Which type of error was made?
16. A public health agency uses a random sample to estimate the proportion of restaurant kitchens that violate a new sanitation rule. The estimate is high enough that the agency considers increasing inspections, which would divert staff from other programs. Why is it important to consider potential error in the estimate when deciding whether to increase inspections?
17. A public health researcher examines whether the number of cigarettes smoked per day ($x$) predicts lung capacity in liters ($y$) among adults. Using a random sample of 55 adults, the researcher fits a least-squares regression line predicting lung capacity from cigarettes per day. The research claim is that smoking more cigarettes is associated with lower predicted lung capacity (negative slope). Which hypotheses are appropriate for testing this claim about the population regression slope?
18. A weather app classifies tomorrow's precipitation for a city as None (N), Rain (R), or Snow (S), so the sample space is $\{N, R, S\}$. The app reports $P(R)=0.25$ for tomorrow. Which statement correctly describes the probability $0.25$ in this context?
19. An airline uses a sample of recent flights to estimate the mean delay time and decides whether to add extra scheduled buffer time. If the true mean delay is lower, adding buffer could reduce competitiveness; if the true mean delay is higher, not adding buffer could increase missed connections. Why is it important to consider potential error when using the sample estimate to make the scheduling decision?
20. A city compares the proportion of residents who support building a new park in two neighborhoods. An SRS of $n_1=40$ residents from Neighborhood 1 and an independent SRS of $n_2=40$ residents from Neighborhood 2 are taken; $\hat p_1$ and $\hat p_2$ are the sample proportions in favor. The sampling distribution of $\hat p_1-\hat p_2$ is considered over many repetitions. Which statement is correct?

Practice tests