Practice Test 58 - AP Statistics

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

A nutrition researcher wanted to test whether a new high-fiber snack reduces afternoon hunger. She recruited 60 volunteers from a gym and matched them into 30 pairs based on age and baseline hunger rating. Within each pair, one person was randomly assigned to eat the high-fiber snack each afternoon for 2 weeks, and the other was randomly assigned to eat a standard snack with the same calories. At the end of 2 weeks, the high-fiber group reported lower average hunger. Which conclusion is justified based on the design of this study?
A teacher compares mean quiz scores for students using two different study apps. Two independent random samples are taken: App A and App B. A two-sample $t$ test for $\mu_A-\mu_B$ is conducted with $H_0: \mu_A-\mu_B=0$ and $H_a: \mu_A-\mu_B\neq 0$ . The p-value is 0.52. At $\alpha=0.05$ , what conclusion is appropriate?
A genetics model predicts that offspring phenotypes should occur in a 9:3:3:1 ratio across four categories. A researcher observes 160 offspring and records the counts in the table. A chi-square goodness-of-fit test is run for $H_0$ : the phenotype distribution follows the 9:3:3:1 ratio vs. $H_a$ : it does not. The p-value is 0.041. What conclusion is appropriate at the $\alpha=0.01$ level? Observed/Expected counts and p-value: - p-value = 0.041
A school compared mean number of absences in a semester for students in an advisory program (A) versus students not in the program (N). From independent random samples, a 98% confidence interval for $\mu_A-\mu_N$ is $(0.4,\ 2.1)$ absences. Which interpretation is correct?
A basketball player shoots exactly 15 free throws during practice. A shot is a success if it goes in. The coach wants to model the number of made shots using a binomial distribution. Does this meet binomial conditions?
A psychology teacher wants to test whether background music affects quiz performance. The teacher has two class periods of the same course (Period 2 and Period 5). Because the teacher cannot play music for some students and not others within the same room at the same time, the teacher must choose one condition per class period on quiz day. Which experimental design is most appropriate?
A museum wants to estimate the mean age of visitors on a particular holiday. Two volunteers each independently select a random sample of 35 visitors from that holiday's attendance list and compute the mean age. Volunteer 1 gets 28.6 years, and Volunteer 2 gets 31.4 years. Both samples were taken from the same holiday and selected randomly. Why might the sample results differ?
A call center estimates that each call is resolved within 10 minutes with probability 0.80, independently. To estimate the probability that in a set of 15 calls, at least 14 are resolved within 10 minutes, a student simulates 5000 sets of 15 calls using random digits (0–7 = resolved, 8–9 = not resolved). The simulation yields 178 sets meeting the condition. Which interpretation of the simulation results is correct?
A manufacturer states that 2% of batteries fail within the first month. Many random samples of $n=100$ batteries are taken and $\hat p$ is recorded each time. Which statement about the sampling distribution is correct?
A medical researcher investigates whether body mass index ( $x$ ) predicts resting heart rate in beats per minute ( $y$ ). The researcher suspects that higher BMI is associated with higher resting heart rate in the population. Which hypotheses are appropriate for testing this claim about the slope of the population regression line predicting $y$ from $x$ ?
A cereal manufacturer advertises that boxes contain an average of $\mu=500$ grams of cereal. A quality-control analyst takes a random sample of 25 boxes and performs a one-sample $t$ test with $H_0:\mu=500$ and $H_a:\mu\neq 500$ using $\alpha=0.01$ . The p-value from the test is 0.043. What conclusion is appropriate?
An educator compares mean exam scores (out of 100) between students taught with Method X and Method Y. Using independent random samples, a 98% confidence interval for $(\mu_X-\mu_Y)$ is $(-1.5,\,4.0)$ . Which interpretation is correct?
A psychologist compares mean reaction time (milliseconds) for participants who drank caffeinated coffee versus decaf. Two independent random samples were taken (Caffeine: $n=22$ ; Decaf: $n=24$ ). A two-sample $t$ test for $\mu_{\text{caf}}-\mu_{\text{dec}}$ used $H_0:\mu_{\text{caf}}=\mu_{\text{dec}}$ and $H_a:\mu_{\text{caf}}<\mu_{\text{dec}}$ . The p-value was 0.20. Using $\alpha=0.05$ , what conclusion is appropriate?
A gym surveyed members about membership plan (Monthly or Annual) and whether they attend at least 3 times per week (Yes or No). The results are shown in a table. Which comparison is appropriate for assessing the relationship between membership plan and frequent attendance using conditional distributions?
A political campaign calls 30 registered voters. For each call, the campaign records whether the voter is reached (success) or not reached (failure). Based on past calling data, the probability of reaching a voter is 0.55, and each call is treated as independent with a constant probability of success. Let $X$ be the number of voters reached. Which values correctly model this situation?
A researcher studies 16 runners, recording $x$ = minutes of stretching before a run and $y$ = time to complete a 5K (minutes). The regression of 5K time on stretching gives a 90% confidence interval for the population slope $\beta$ of $(-0.25,\ 0.05)$ . Which interpretation is correct?
A manager regresses monthly sales (in dollars) on number of online ads purchased using a random sample of 45 months. A 92% confidence interval for the slope is $(120,\ 480)$ dollars per ad. Which interpretation is correct?
A researcher records the number of defective batteries in a randomly selected pack of 6 batteries. Let $X$ be the number of defective batteries in the pack. The probability distribution of $X$ is given in the table. Which statement correctly interprets the random variable $X$ ?
A teacher believes students choose among 4 project topics equally often. In a random sample of 80 students, the topic choices are recorded and a chi-square goodness-of-fit test is run for $H_0$ : all 4 topics are equally likely versus $H_a$ : not all are equally likely. The p-value is 0.20. The observed and expected counts are shown. What conclusion is appropriate at the $\alpha=0.10$ level?
For the population of bottles filled by a machine, fill volumes are approximately Normal with mean $\mu=500$ mL and standard deviation $\sigma=4$ mL. A quality-control rule marks bottles in the interval 492 mL to 508 mL. Which statement about the marked interval is correct?

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