Practice Test 21 - AP Statistics

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

A biologist captures a random sample of 200 fish from a lake and classifies each fish by species (trout/bass/perch/catfish). She wants to test whether the distribution of species in the lake matches a state report claiming proportions of 0.40 trout, 0.30 bass, 0.20 perch, and 0.10 catfish. Which inference procedure is most appropriate?
A school compares quiz scores. Let $X$ be a student's score on Quiz 1 and $Y$ be the score on Quiz 2. Assume $X$ and $Y$ are independent, with $\mu_X=78$ , $\sigma_X=10$ , $\mu_Y=82$ , and $\sigma_Y=12$ . Define $A=(X+Y)/2$ , the average of the two quiz scores. Which statement about $A$ is correct?
A state health department wants to estimate the mean number of sugary drinks consumed per week by all adults in the state. Investigators interview every 10th adult who enters a large grocery store on Saturday morning, starting with the 3rd adult who enters, and collect 260 interviews. Which statement best describes the sample representativeness?
A researcher compares mean reaction time (milliseconds) for participants who drank coffee (C) versus water (W). A 95% confidence interval for $\mu_C-\mu_W$ is $(-35,\ 5)$ . The researcher claims coffee leads to a faster (smaller) mean reaction time than water. Is the claim supported by the interval?
A survey indicates that 58% of residents support building a new library. A pollster repeatedly takes many random samples of $n=250$ residents and computes $\hat p$ . Which statement about the sampling distribution is correct?
A gym owner tests whether class format affects calories burned. The observational units are 75 participants, each attending exactly one class. For each participant, the owner records class format (in-person or virtual), calories burned (from a fitness tracker), and membership ID number. The goal is to determine if class format helps explain variation in calories burned. Which classification is correct for class format and calories burned?
A state agency wants to estimate the mean number of hours per week that all adults in the state exercise. The agency uses a random-digit dialing method to call phone numbers and interviews the first 600 adults who answer and agree to participate. Which statement best describes the sample representativeness?
A wildlife biologist wants to estimate the population mean weight $\mu$ of adult fish in a lake. The biologist catches fish using a net with holes large enough that very small fish often escape before being weighed. The point estimate is the sample mean $\bar{x}$ of the weights of the 70 fish that are successfully caught and weighed. Which statement describes whether the estimate is biased?
A manufacturer measures the number of defects per roll of fabric. The population distribution is heavily right-skewed, with many rolls having 0–1 defects and a few having a large number. A random sample of $n=50$ rolls is taken, and the mean number of defects is computed. Why is the sampling distribution of $\bar{x}$ approximately normal?
Imagine a population where for any given value of an explanatory variable $x$ , there is a distribution of corresponding values for a response variable $y$ . If a linear relationship exists, the means of these distributions fall on a straight line. Why would individual points from this population not fall perfectly on that line?
A fitness researcher uses a least-squares line to predict resting heart rate ( $y$ ) from weekly minutes of aerobic exercise ( $x$ ) for 80 adults. The researcher claims that more exercise is associated with a lower mean resting heart rate. A 99% confidence interval for the slope is $(-0.09, -0.01)$ beats per minute per minute of exercise. Is the claim supported by the confidence interval?
A bottling plant fills 20-oz bottles with a long-run mean fill of $\mu=20.0$ oz and a population standard deviation of $\sigma=0.6$ oz. The distribution of individual fill amounts is right-skewed. An inspector repeatedly takes simple random samples of size $n=36$ bottles and computes the sample mean $\bar{x}$ each time. Which statement about the sampling distribution of $\bar{x}$ is correct?
A marketing analyst studies whether the number of ads shown to a user is related to the amount the user spends on a website. For a random sample of 70 users, the analyst records ads shown (explanatory variable $x$ ) and dollars spent (response variable $y$ ) and fits a least-squares regression line predicting spending from ads. The analyst's claim is that showing more ads reduces spending, so the population slope is negative. Which hypotheses are appropriate for testing this claim about the slope?
A public health researcher studied $n=50$ adults and recorded weekly minutes of exercise ( $x$ ) and resting heart rate ( $y$ , beats per minute). A least-squares regression of heart rate on exercise produced slope $b_1=-0.05$ . The researcher tested $H_0: \beta_1=0$ versus $H_a: \beta_1<0$ and obtained a p-value of $0.0019$ . Based on this completed slope test, what conclusion is appropriate?
A wildlife biologist studies a pond and defines $X$ as the number of frogs heard croaking during a 5-minute audio recording made at sunset on a randomly selected day. The distribution of $X$ has mean $\mu_X=18.6$ croaks and standard deviation $\sigma_X=4.0$ croaks. Which interpretation of the standard deviation is correct?
A city traffic engineer investigates whether road surface type affects braking distance on wet roads. The observational units are 60 test runs, each using the same car at 35 mph. For each run, the engineer records surface type (asphalt or concrete), braking distance in feet, and run number (1–60). The goal is to determine if surface type explains variation in braking distance. Which classification is correct for surface type and braking distance?
The time (in minutes) that customers spend waiting in line at a busy coffee shop during the morning rush is approximately Normal with mean $\mu=6.0$ and standard deviation $\sigma=1.5$ . The normal curve below marks a wait time of 7.5 minutes. Which statement about the marked value is correct?
A physicist studies whether the length of a pendulum in meters ( $x$ ) predicts its period in seconds ( $y$ ). The physicist claims that longer pendulums have longer periods in the population. Which hypotheses are appropriate for testing this claim about the slope in the regression of $y$ on $x$ ?
A delivery company recorded the distance (in miles) of each of 30 delivery routes completed in one day, using GPS totals for each route. The dotplot below shows the distribution of route distances. Which feature of the distribution is most evident?
A hospital tests whether a new discharge checklist reduces the proportion of patients readmitted within 30 days. Under the old process, a random sample of 260 patients had 52 readmissions. Under the new checklist, a separate random sample of 240 patients had 34 readmissions. A two-proportion $z$ test was performed for $H_0: p_{old}=p_{new}$ versus $H_a: p_{old}>p_{new}$ , and the p-value was 0.047. Using $\alpha=0.05$ , what conclusion is appropriate?

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