Practice Test 65 - AP Statistics

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

A game app records that the probability a player wins a particular level on any given attempt is $P(\text{Win})=0.65$ . For one attempt, the sample space is $\{\text{Win},\text{Lose}\}$ , and the event of interest is Win. Which statement correctly interprets the probability $0.65$ ?
An environmental group estimates the proportion $p$ of households in a town that regularly recycle. In a random sample of 150 households, 93 say they regularly recycle. A 92% confidence interval for $p$ is $(0.54, 0.70)$ . Which interpretation is correct?
Let $X$ be the discrete random variable representing the number of goals scored by a soccer team in a match. Over a season, the distribution of $X$ has $\mu_X=1.8$ and $\sigma_X=1.2$ . Which interpretation of the standard deviation is correct?
A coffee shop claims the mean amount of coffee dispensed per "large" cup is $\mu=16$ oz. A manager takes a random sample of cups and computes a 90% confidence interval for $\mu$ as $(15.6,\ 15.9)$ oz. Is the claim supported by the confidence interval?
A nutritionist records daily sodium intake (mg) $x$ and systolic blood pressure (mmHg) $y$ for 18 adults and fits a least-squares regression line to predict blood pressure from sodium intake. Which statement about the regression line is correct?
A marketing team wants to compare brand preference among four age groups (18–29, 30–44, 45–59, 60+). They take independent random samples from each age group and ask which of three brands (X, Y, Z) each person prefers. The results are shown. Which test is appropriate, and what are the correct hypotheses?
A researcher examines whether daily screen time ( $x$ , hours) predicts number of hours slept ( $y$ ) for 40 randomly selected adults. A regression of sleep on screen time is fit, and a slope test is carried out with $H_0: \beta_1=0$ versus $H_a: \beta_1\neq 0$ . The output reports a two-sided p-value of 0.003. At $\alpha=0.01$ , the researcher rejects $H_0$ . What conclusion is appropriate?
A nutrition researcher studies whether daily fiber intake ( $x$ , in grams) predicts total cholesterol ( $y$ , in mg/dL) among 80 adults. A least-squares regression of cholesterol on fiber intake is fit. The researcher's claim is that higher fiber intake is associated with lower average cholesterol, but wants to use a two-sided alternative in case the association is in the opposite direction. Which hypotheses are appropriate for testing the slope of the population regression line?
A teacher summarized scores (out of 100) on a quiz for 40 students. The summaries were: mean $=76.1$ , median $=78.0$ , SD $=8.9$ , $Q_1=72.0$ , $Q_3=82.0$ , minimum $=50$ , maximum $=90$ (five-number summary: $50, 72, 78, 82, 90$ ). Which interpretation is correct?
A sports scientist wants to compare the mean vertical jump height (in cm) of students who completed a 6-week plyometrics program versus students who followed their usual training. A random sample of $n=30$ plyometrics students had a mean jump height of $\bar{x}=52.4$ cm, and a random sample of $n=28$ usual-training students had a mean jump height of $\bar{x}=48.9$ cm. The scientist's research claim is that the plyometrics program increases the population mean jump height. Which hypotheses are appropriate?
A state university wants to estimate the proportion of all undergraduate students who support a proposed change to the general education requirements. The university's registrar has a list of all undergraduates and randomly selects 400 student ID numbers. The researcher emails those 400 students, but 120 emails bounce back due to outdated addresses, and the researcher surveys only the remaining 280 students. Which statement best describes the sample representativeness?
A transportation planner studies whether commute distance predicts commute time. From a random sample of 70 commuters, the planner records commute distance in miles ( $x$ ) and commute time in minutes ( $y$ ), then fits a least-squares regression line predicting time from distance. The research claim is that there is a linear relationship between distance and time (slope differs from 0). Which hypotheses are appropriate for testing this claim about the population regression slope?
A teacher wants to know whether students in her AP Statistics class sleep more on weekends than on school nights. She asks all 28 students in her class to report how many hours they slept last night (a school night) and how many hours they slept the most recent Saturday night. The average reported increase (Saturday minus school night) is 1.6 hours. Which conclusion is supported by these data?
A political scientist claims that support for three candidates in a district is 35% for Candidate A, 40% for Candidate B, and 25% for Candidate C. A random sample of 240 likely voters is surveyed. A chi-square goodness-of-fit test is performed for $H_0$ : the population proportions match 0.35/0.40/0.25 versus $H_a$ : they do not. The p-value is 0.057. The observed and expected counts are shown. What conclusion is appropriate at the $\alpha=0.05$ level?
A university compared the proportion of applicants who accept an admission offer under two different financial-aid email formats. In a random sample of 260 admitted applicants sent Email Format A, 143 accepted; in a random sample of 240 admitted applicants sent Email Format B, 150 accepted. A two-proportion $z$ test was performed for $H_0: p_A=p_B$ versus $H_a: p_A\ne p_B$ , and the p-value was $0.08$ . Using $\alpha=0.05$ , what conclusion is appropriate?
A school compares the proportion of students who prefer online homework in two grades. Let $p_9$ be the true proportion for 9th graders and $p_{12}$ for 12th graders. A 95% confidence interval for the difference in proportions, computed as $p_9-p_{12}$ , is $(0.04,\ 0.18)$ . A student claims, "A higher proportion of 9th graders than 12th graders prefer online homework." Is the claim supported by the interval?
A sports scientist models a runner's 5K time (minutes) from the number of weeks in a training program. The scientist claims that training reduces 5K time by between 0.10 and 0.30 minutes per week. A 95% confidence interval for the slope is $(-0.28, -0.12)$ minutes per week. Is the claim supported by the confidence interval?
A bottled water company states that the mean volume in its 500 mL bottles is 500 mL. Inspectors take a random sample of $n=50$ bottles and measure a sample mean of $\bar{x}=498.6$ mL. They want to test whether the true mean volume is different from 500 mL. Which hypotheses are appropriate for a test of a population mean?
A tech company claims that 90% of its deliveries arrive on time. Many random samples of $n=40$ deliveries are taken over time and $\hat p$ is computed for each sample. Which statement about the sampling distribution is correct?
A scientist compares mean plant growth (cm) under two fertilizers. She takes an independent random sample of $n_F=20$ plants with Fertilizer F and $n_G=80$ plants with Fertilizer G, then considers the sampling distribution of $\bar{x}_F-\bar{x}_G$ . Which statement is correct about the standard deviation of $\bar{x}_F-\bar{x}_G$ ?

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