Practice Test 97 - AP Statistics

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

A nutrition scientist wants to test whether drinking a caffeinated beverage affects reaction time. Forty participants come to the lab twice, one week apart. Each participant is randomly assigned to drink caffeine on the first visit and decaf on the second visit, or decaf first and caffeine second. Reaction time is measured 30 minutes after the drink on each visit. Which design principle is primarily being used by having every participant receive both treatments in random order?
A wildlife biologist expects that 25% of a certain fish species in a lake carry a harmless parasite. She catches and tests 80 fish at random, expecting about 20 positives, but finds 30 positives. Assuming the true rate is 25% and fish are sampled independently, is this result unexpected given sampling variability with $n=80$ ?
A public library randomly selects one book returned today and records whether it is "On time," "Late," or "Damaged." The sample space is {On time, Late, Damaged}. Let L be the event that the book is late. The library estimates $P(L)=0.18$ . Which statement correctly describes the probability?
A school compares two study apps by randomly assigning students to use App A or App B for one week. Many repetitions of the process are imagined: each time, a random sample of $n_A=40$ students uses App A and a random sample of $n_B=40$ students uses App B, and the difference in sample means $\bar{x}_A-\bar{x}_B$ (quiz score points) is recorded. Which statement about the sampling distribution of $\bar{x}_A-\bar{x}_B$ is correct?
An environmental group is comparing mean nitrate concentration (in mg/L) in water samples taken from two rivers. A random sample of 18 sites along River 1 had a mean nitrate concentration of 3.8 mg/L, and a random sample of 20 sites along River 2 had a mean of 3.1 mg/L. The research claim is that River 1 has a higher mean nitrate concentration than River 2. Which hypotheses are appropriate?
To perform a chi-square test for independence, the company needs to calculate expected counts. What is the expected number of users with OS A who primarily use gaming apps, assuming OS and primary app type are independent?
A university randomly selects a student from those enrolled in an introductory statistics course. Let event $A$ be "the student attends the optional review session," and event $B$ be "the student is on an athletic team." At this university, athletes have less free time and historically attend the review session at a lower rate than the class overall. How does knowing that $B$ occurred affect the likelihood of $A$ ?
A student flips a biased coin once and records the outcome: Heads (H) or Tails (T), so the sample space is $\{H, T\}$ . The coin has probability $P(H)=0.60$ . Which statement correctly describes the probability $0.60$ in this context?
A manufacturer states that defects in a production line fall into 4 categories with population proportions: 0.10 Scratch, 0.20 Dent, 0.30 Paint, 0.40 Other. In a random sample of 200 defects, the observed counts are Scratch 28, Dent 36, Paint 59, Other 77. A chi-square goodness-of-fit test of $H_0$ : the defect-type distribution matches the stated proportions yields $p$ -value = 0.061. Expected counts under $H_0$ are Scratch 20, Dent 40, Paint 60, Other 80. What conclusion is appropriate at $\alpha=0.05$ ?
A streaming service claims that fewer than 25% of its subscribers cancel within the first month. A random sample of 400 new subscribers shows that 112 canceled within the first month (so $\hat{p}=0.28$ ). Which hypotheses are appropriate for testing whether the true population proportion $p$ of first-month cancellations is greater than the service's claim?
An environmental scientist records daily high temperatures (in $^\circ$ F) for 31 days in July in one city. The five-number summary is: min $=71$ , $Q_1=78$ , median $=83$ , $Q_3=88$ , max $=97$ . A boxplot is drawn from these values. Which feature is consistent with the summary statistics?
A city's transportation department believes that cars arrive at a toll booth in the following proportions: 25% compact, 45% midsize, 30% SUV. A random sample of 160 cars is classified. A chi-square goodness-of-fit test is conducted for $H_0$ : the population distribution matches the stated proportions versus $H_a$ : it does not. The p-value from the test is 0.41. The observed and expected counts are shown. What conclusion is appropriate at the $\alpha=0.05$ level?
A student researches whether the number of pages read for a class ( $x$ ) predicts the time spent studying in hours ( $y$ ). The student believes that reading more pages is associated with more study time in the population. Which hypotheses are appropriate for testing this claim about the slope in the regression of $y$ on $x$ ?
A biology lab expects a 1:2:1 ratio of flower colors (white:pink:red) in a large population of plants. A random sample of 80 flowers is observed, and a chi-square goodness-of-fit test is conducted at $\alpha=0.05$ . The results are below. What conclusion is appropriate? Observed/Expected counts and p-value: - White: Observed 18, Expected 20 - Pink: Observed 44, Expected 40 - Red: Observed 18, Expected 20 - p-value = 0.54
A company tests two advertising designs and records the mean number of website visits per day. Design 1 had a sample mean of 510 visits and Design 2 had a sample mean of 525 visits. A 90% confidence interval for the difference in population means, defined as $\mu_1-\mu_2$ , is $(-30, -5)$ . A manager claims, "Design 1 results in fewer mean daily visits than Design 2." Is the claim supported by the confidence interval?
A wildlife biologist tests whether the proportion of a fish species carrying a parasite is less than 0.30. The hypotheses are $H_0: p=0.30$ versus $H_a: p<0.30$ at $\alpha=0.05$ . The test is statistically significant, so the biologist concludes the parasite rate is below 0.30. In reality, the true population proportion is $p=0.34$ . Which type of error was made?
A mechanic studies whether tire pressure in psi ( $x$ ) predicts gas mileage in miles per gallon ( $y$ ). The mechanic believes that higher tire pressure (within safe limits) increases gas mileage in the population. Which hypotheses are appropriate for testing this claim about the slope of the population regression line?
Let $X$ be the discrete random variable representing the number of absences a randomly selected student has in a semester. At a school, $\mu_X=2.3$ absences and $\sigma_X=2.0$ absences. Which interpretation of the mean is correct?
A technology company claims that the proportion of users who enable two-factor authentication is $p = 0.35$ . A random sample of users is selected and a one-proportion test is performed for $H_0: p = 0.35$ versus $H_a: p > 0.35$ at $\alpha = 0.05$ . The p-value is $p = 0.006$ . Which interpretation of the p-value is correct?
A teacher studies whether students' quiz average (percent) can be predicted from the number of class absences during a grading period. From a random sample of 40 students, the teacher fits a least-squares regression with quiz average as the response and absences as the explanatory variable. The teacher's claim is that more absences are associated with lower average quiz scores in the population, implying a negative population slope. Which hypotheses are appropriate for testing this claim about the slope?

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