Practice Test 96 - AP Statistics

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

A pollster calls 60 phone numbers and records whether each person reached agrees to participate. A success is "agrees," and the pollster makes exactly 60 calls, but stops calling early if 30 people agree. Does this meet binomial conditions for modeling the number of successes?
What is the primary purpose of constructing and analyzing a residual plot in a linear regression analysis?
A tech company believes that fewer than 10% of its employees work remotely full-time. A random sample of 250 employees finds that 32 work remotely full-time. A one-sample $z$ test for a population proportion is conducted at $\alpha=0.05$ with $H_0:p=0.10$ and $H_a:p<0.10$ . The test produces a $p$ -value of 0.96, so the decision is to fail to reject $H_0$ . Which conclusion is appropriate?
A city estimates that 68% of commuters drive alone. Many random samples of $n=160$ commuters are taken and $\hat p$ is computed each time. Which statement about the sampling distribution is correct?
A runner tracked the time (in minutes) it took to complete a particular 5K route on 26 different days. The dotplot below shows the distribution of times. Which statement best describes the distribution?
A city compares mean commute times (minutes) for residents who take public transit versus those who drive. An SRS of $n_1=100$ transit riders and an independent SRS of $n_2=100$ drivers are taken, and $\bar{x}_T-\bar{x}_D$ is computed. Suppose the population standard deviations are $\sigma_T$ and $\sigma_D$ . Which statement is correct?
A company advertises that 60% of its customers renew their subscription. A random sample of 200 customers finds 112 renewals. A one-proportion $z$ test is conducted for $H_0: p = 0.60$ versus $H_a: p \ne 0.60$ at $\alpha = 0.10$ , yielding p-value $p = 0.041$ . Which interpretation of the p-value is correct?
A sociologist studies whether the number of hours spent on social media per day ( $x$ ) predicts self-reported stress level ( $y$ ) on a 1–10 scale. The sociologist claims that more social media time is associated with higher stress in the population. Which hypotheses are appropriate for testing this claim about the regression slope?
A teacher records the number of absences ( $x$ ) and final course average ( $y$ , percent) for 16 students. A least-squares regression line is fit to predict course average from absences: $\hat{y}=92.6-1.8x$ . The purpose of this linear model is to describe the linear pattern and predict typical course averages for absence counts similar to those observed. Which interpretation of the model is correct?
For the population of adult women in a city, resting heart rates are approximately Normal with mean $\mu=72$ beats per minute and standard deviation $\sigma=12$ beats per minute. A clinic flags anyone with a resting heart rate below 48 bpm for follow-up. Which statement about the marked value is correct?
Let $C$ be the amount (in dollars) Casey spends on coffee in a week and $S$ be the amount (in dollars) Casey spends on snacks in a week. Over many weeks, $\mu_C=18$ with $\sigma_C=4$ , and $\mu_S=22$ with $\sigma_S=5$ . Assume $C$ and $S$ are independent. Define $N=C-S$ . Which statement about $N$ is correct?
A state agency wants to estimate the proportion of registered voters who support a particular ballot measure. Two independent random samples were drawn from the same statewide voter registration database. Sample 1 (n = 500) found 49% support; Sample 2 (n = 500) found 53% support. The question wording and sampling method were identical. Why might the sample results differ?
In a survey, 48% of respondents prefer Brand X, 42% prefer Brand Y, and 10% prefer both (they said either would be fine). Let Event A be "a randomly selected respondent prefers Brand X" and Event B be "the respondent prefers Brand Y." Which statement about Events A and B is correct?
A cereal company advertises that 25% of its boxes contain a coupon for a free prize. A consumer group suspects the true proportion is lower. They randomly select 120 boxes and find 22 with coupons (so $ \hat{p}=22/120$). Which hypotheses are appropriate for a one-proportion test?
A farmer recorded the weights (in pounds) of 50 pumpkins harvested from one field. The summaries were: mean $=18.6$ lb, median $=16.9$ lb, SD $=7.4$ lb, $Q_1=13.2$ lb, $Q_3=21.0$ lb, minimum $=6.0$ lb, maximum $=44.0$ lb (five-number summary: $6.0, 13.2, 16.9, 21.0, 44.0$ ). Which interpretation is correct?
A real estate analyst fits a regression line with home sale price (in thousands of dollars) as the response and home size (in square feet) as the explanatory variable, using a random sample of recent sales in a city. A 95% confidence interval for the population slope is $(0.08,\ 0.14)$ . Which interpretation is correct?
A tech company compares the proportion of users who enable two-factor authentication on two platforms. Platform W: SRS of $n_W=1000$ users; Platform M: independent SRS of $n_M=1000$ users. The statistic is $\hat{p}_W-\hat{p}_M$ . Suppose $p_W$ and $p_M$ stay the same over time and the sampling method stays the same. Which statement is correct about what would happen to the sampling distribution if both sample sizes were reduced to $n_W=n_M=100$ ?
A company reports that 66% of its employees participate in a retirement plan. Many random samples of $n=120$ employees are taken and $\hat p$ is recorded. Which statement about the sampling distribution is correct?
A school nurse recorded the number of absences per student for all students in one grade during a semester. The five-number summary was: min $=0$ , $Q_1=1$ , median $=2$ , $Q_3=4$ , max $=15$ . A boxplot is made using whiskers to the minimum and maximum (no separate outlier marking). Which feature is consistent with the summary statistics?
A psychologist studies, for 25 adults, hours of sleep per night (hours) and stress score (on a 0–50 scale). The scatterplot shows a moderate negative linear association. Which statement about correlation is correct?

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