Practice Test 35 - AP Statistics

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

A student takes a 4-question multiple-choice quiz where each question is either correct or incorrect. Let the discrete random variable $X$ be the number of questions answered correctly on the quiz. The probability distribution of $X$ is shown in a table. Which statement correctly interprets the random variable $X$ ?
A teacher recorded quiz scores (out of 20 points) for 30 students. The summary statistics were: mean $= 14.2$ , median $= 15.5$ , standard deviation $= 3.6$ , five-number summary $(2, 13, 15.5, 18, 20)$ , and IQR $= 5$ . Which interpretation is correct?
Assuming no association exists between region and favorite season, what is the expected number of residents from the South who would choose Summer as their favorite season?
A public health researcher studies whether neighborhoods with more walkable streets tend to have lower average body mass index (BMI). For a random sample of 60 neighborhoods, the researcher records walkability score (explanatory variable $x$ ) and mean adult BMI (response variable $y$ ) and fits the least-squares regression line to predict BMI from walkability. The research claim is that higher walkability is associated with lower mean BMI, meaning the population slope is negative. Which hypotheses are appropriate for testing this claim about the slope of the population regression line?
A spinner is divided into 8 equal sectors labeled 1 through 8. The spinner is spun once. Let Event A be "the result is a multiple of 2" and Event B be "the result is a multiple of 4." Which statement about Events A and B is correct?
A streaming service wants to estimate the mean number of hours per week that all subscribers watch content. The service randomly selects 2,000 subscriber accounts from its full subscriber database and uses server logs to compute each selected account's viewing hours for the past week. Which statement best describes the sample representativeness?
In the American legal system, a defendant is presumed innocent until proven guilty. If a criminal trial is viewed as a hypothesis test where the claim to be tested is that the defendant is guilty, what would be the null and alternative hypotheses?
A quality-control manager tests whether the mean fill amount for a brand of cereal differs from the labeled 16 oz. A random sample of 40 boxes is taken, and conditions for a one-sample $t$ test are met. The hypotheses are $H_0: \mu=16$ and $H_a: \mu\neq 16$ at significance level $\alpha=0.05$ . The test is completed and the p-value is 0.032. What conclusion is appropriate?
A teacher models number of practice problems completed ( $x$ ) and quiz score ( $y$ ) with a least-squares regression line to predict quiz score from practice. A scatterplot with the fitted line is shown. Which statement about the regression line is correct?
A student is testing the hypotheses $H_0: p = 0.80$ versus $H_a: p > 0.80$ using a sample of 100 individuals. The student finds a sample proportion of $\hat{p} = 0.85$ . The student checks the Large Counts condition by calculating $100(0.85) = 85$ and $100(0.15) = 15$ , noting both are greater than 10. What is the flaw in this procedure?
A teacher compares mean quiz scores for two different teaching methods. She randomly assigns students to Method 1 and Method 2, then records quiz scores. Suppose $n_1=50$ and $n_2=50$ , and she computes $\bar{x}_1-\bar{x}_2$ . Which statement is correct about the center of the sampling distribution of $\bar{x}_1-\bar{x}_2$ ?
A city wants to estimate the percentage of households that recycle weekly. Two independent simple random samples are selected from the same list of all city households. Sample A of 200 households finds 61% recycle weekly; Sample B of 200 different households finds 56%. Why might the sample results differ?
In a state, the systolic blood pressure (in mmHg) for all adults is approximately Normal with mean $\mu=120$ and standard deviation $\sigma=15$ . A value is marked at $x=150$ mmHg. Which statement about the marked value is correct?
A teacher gives a 10-question multiple-choice quiz. For each question, a particular student either answers correctly (success) or incorrectly (failure). However, the student is more likely to answer later questions correctly because the questions get easier as the quiz goes on. The teacher records the number correct out of 10. Does this meet the binomial conditions?
A marketing analyst wants to estimate the mean amount (in dollars) customers spend per visit at a coffee shop chain. She takes a random sample of 45 customers and constructs a 95% confidence interval for the population mean spending: ($4.80, $5.40). Which interpretation is correct?
A student randomly samples 10 files from a computer containing 60 files and records whether each file is corrupted. A success is "corrupted," and exactly 10 files are sampled without replacement. Does this meet binomial conditions?
A restaurant manager wants to know whether day of the week is related to customer wait time. For each of 100 parties (observational units), the manager records the day (Mon–Sun) and the wait time in minutes before being seated. The goal is to see if wait times differ by day. Which classification is correct?
A commuter takes a train that can arrive "Early," "On time," or "Late." The sample space is {Early, On time, Late}. Let T be the event that the train is on time. Based on historical data, $P(T)=0.62$ . Which statement correctly describes the probability?
In a school cafeteria, let $X$ be the number of minutes a randomly selected student waits in the lunch line on Monday, with mean $\mu_X=8$ and standard deviation $\sigma_X=2$ . Let $Y$ be the number of minutes a randomly selected student waits in the lunch line on Tuesday, with mean $\mu_Y=10$ and standard deviation $\sigma_Y=3$ . Assume $X$ and $Y$ are independent. Define the combined variable $T=X+Y$ as the total waiting time over the two days. Which statement about the combined variable is correct?
A school district compares the mean number of minutes of homework completed on a weeknight by students in two programs. A random sample of $n=38$ students in the tutoring program had a mean of $\bar{x}=52.1$ minutes, and a random sample of $n=41$ students not in tutoring had a mean of $\bar{x}=47.6$ minutes. The district's research claim is that students in tutoring complete more homework on average. Which hypotheses are appropriate for testing the claim about the population means?

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