Practice Test 45 - AP Statistics

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

A gym advertises that the mean number of calories burned in its 45-minute cycling class is 400 calories. A member suspects the true mean calories burned is less than 400. The member records calories burned for a random sample of 12 classes and finds a sample mean of 385 calories. Which hypotheses are appropriate for a one-sample test of a population mean calories burned?
A company wants to test two versions of an online checkout page (Version 1 vs Version 2) on purchase completion rate. Customer device type (mobile vs desktop) is known to affect purchasing behavior, and the company can randomize which version a customer sees when they arrive. Which experimental design is most appropriate?
A museum claims that visitors' favorite exhibit is distributed as 30% Ancient History, 25% Modern Art, 20% Science, 15% Nature, and 10% Technology. A random sample of 400 visitors is surveyed, and the observed counts are shown in the table. Which hypotheses are appropriate for a chi-square goodness-of-fit test? Observed counts table (n = 400): Ancient 132, Modern Art 88, Science 70, Nature 66, Technology 44.
A teacher records number of absences $x$ and final course grade (percent) $y$ for students in a class and fits the least-squares regression line to predict grade from absences. Which statement about the regression line is correct?
A software tester runs an automated test suite repeatedly until the first time a critical error occurs. Each run results in either "critical error" or "no critical error," and the tester stops after the first critical error. Assume the probability of a critical error is the same on each run and runs are independent. The tester wants to model the number of runs until the first critical error. Why is a geometric model appropriate?
A cereal company advertises that 40% of boxes contain a "bonus card." A teacher buys 10 boxes for a class activity, expecting about 4 bonus cards, but finds 9 bonus cards. Assuming the 40% rate is accurate and each box is independent, is this result unexpected given natural sample-to-sample variability?
A school district compared the proportion of students who pass a math proficiency exam in two independent random samples: 44 of 80 students from School X passed and 70 of 140 students from School Y passed. A two-proportion $z$ test was conducted at $\alpha=0.05$ to test $H_0: p_X=p_Y$ versus $H_a: p_X>p_Y$ , where $p_X$ and $p_Y$ are the true passing proportions at Schools X and Y. The p-value was 0.12. What conclusion is appropriate?
A student's commute time is the sum of bus wait time $W$ and bus ride time $R$ (in minutes). Assume $W$ and $R$ are independent with $\mu_W=6$ , $\sigma_W=2$ , $\mu_R=18$ , and $\sigma_R=4$ . Let $T=W+R$ . Which statement about $T$ is correct?
A school counselor records the heights (in inches) of a simple random sample of 60 tenth-grade students to understand typical height at the school. The histogram of the 60 heights is roughly unimodal and fairly symmetric with no extreme outliers. Why is a normal model reasonable for these data?
A teacher records the heights (in cm) of a simple random sample of 60 students at a large high school to estimate the distribution of student heights. The histogram of the sample is roughly unimodal and fairly symmetric, with no extreme outliers. Why is a normal model reasonable for these data?
A sports scientist records $n=32$ runners and fits a regression model predicting 5K time ( $y$ , minutes) from weekly training mileage ( $x$ ). The scientist claims that, in the population, more training mileage tends to reduce 5K time (negative slope). Which hypotheses are appropriate for testing this claim about the slope parameter?
A phone manufacturer claims that no more than 8% of its new phones are defective. A quality inspector wants to test whether the defect rate exceeds this value. In a random sample of 500 phones, 52 are found to be defective (so $ \hat{p}=52/500$). Which hypotheses are appropriate?
A nonprofit compares the proportion of donors who give again the next year for two outreach strategies. A 95% confidence interval for the difference in proportions, defined as $p_{Email} - p_{Phone}$ , is $( -0.12,\ -0.02)$ . A director claims, "The email strategy has a lower repeat-donation rate than the phone strategy." Is the claim supported by the confidence interval?
A coin is flipped once and the outcome is recorded. Let event $A$ be "the flip results in Heads" and event $B$ be "the flip results in Tails." A single flip cannot be both Heads and Tails. Are the two events mutually exclusive?
Scores on a certain statewide math assessment for the population of 10th graders are approximately Normal with mean $\mu=500$ and standard deviation $\sigma=100$ . The marked value is $x=350$ . Which statement about the marked value is correct?
A machine is designed to randomly sort identical balls into 2 bins, Left (L) or Right (R), with equal probability each time. A supervisor records the results for 20 balls and sees: L, R, L, R, L, R, L, R, L, R, L, R, L, R, L, R, L, R, L, R. Under random behavior, you would expect some short runs and occasional repeats, not perfect alternation for a long stretch. Is the pattern consistent with random behavior?
A game app records how many hints a randomly selected player uses to finish a level. Let $X$ be the number of hints, a discrete random variable with distribution: $P(X=0)=0.25$ , $P(X=1)=0.40$ , $P(X=2)=0.20$ , $P(X=3)=0.10$ , $P(X=4)=0.05$ . The mean is $\mu_X=1.30$ hints and the standard deviation is $\sigma_X=1.17$ hints. Which interpretation of the mean is correct?
An economist models the relationship between a country's GDP and its average life expectancy using a linear regression model on data from a sample of countries. After fitting the line, she observes that the residuals are all positive for low and high GDPs and negative for mid-range GDPs. What does this pattern suggest about the linear model?
A city's transportation office claims that commuters use the following primary modes of transportation: 50% drive alone, 20% carpool, 15% public transit, 10% bike, and 5% walk. A random sample of 400 commuters is taken and the observed counts are shown below. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the office's claim?
A city council wants to know whether a new text-message reminder system increased the proportion of residents who pay parking tickets within 14 days. Before the system, 180 of 400 randomly selected ticketed residents paid within 14 days; after the system, 210 of 400 randomly selected ticketed residents paid within 14 days. A two-proportion $z$ test for $H_0: p_{\text{before}}-p_{\text{after}}=0$ versus $H_a: p_{\text{before}}-p_{\text{after}}<0$ produced a p-value of $0.006$ . Using $\alpha=0.05$ , what conclusion is appropriate?

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