Practice Test 27 - AP Statistics

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

A school district wants to determine whether the mean SAT Math score for its seniors is below the national mean of $\mu=520$ . A random sample of 60 seniors is selected, and a one-sample $t$ test is conducted with $H_0:\mu=520$ versus $H_a:\mu<520$ at $\alpha=0.05$ . The p-value is 0.041. What conclusion is appropriate?
A school district pilots an online tutoring program in a sample of classes and finds a statistically significant increase in average math scores compared with classes without tutoring. Leaders consider expanding the program districtwide, which would require cutting another program to pay for it. Why is it important to consider potential error in the inference before making the decision?
A manufacturer compared defect rates for two production lines using independent random samples. Line 1 had 18 defects in a sample of 300 items; Line 2 had 9 defects in a sample of 250 items. A two-proportion $z$ test at $\alpha=0.05$ tested $H_0: p_1=p_2$ versus $H_a: p_1>p_2$ , where $p_1$ and $p_2$ are the true defect proportions for Lines 1 and 2. The p-value was 0.03. What conclusion is appropriate?
A cafeteria manager wants to know whether meal plan is related to number of lunches purchased per week. Students are classified by meal plan (None, 5-meal, Unlimited), and each student reports how many lunches they purchased last week (0–7). The observational units are students, and the goal is to compare lunch purchases across meal plans. Which classification is correct?
What is the best interpretation of this value?
A school nurse wants to know whether the proportion of students who report getting at least 8 hours of sleep on school nights differs between students who participate in after-school sports and students who do not. In a random sample, 78 of 150 sports participants reported at least 8 hours, and 64 of 160 non-participants reported at least 8 hours. The nurse's research claim is that the true proportions are different. Which hypotheses are appropriate?
A professor records the final exam scores (out of 100) for a random sample of 58 students from several sections of the same course. The scores form a single mound and are approximately symmetric. Why is a normal model reasonable for summarizing and comparing these exam scores?
A website tracks whether a visitor is on a mobile device and whether they make a purchase. Let Event $A$ be "visitor is on mobile," and Event $B$ be "visitor makes a purchase." The site reports that $P(B\mid A)=P(B)$ . Which statement about Events $A$ and $B$ is correct?
A random sample of 350 passengers on a commuter rail line found that 210 purchased their ticket using a mobile app. A 94% confidence interval for the true proportion $p$ of all passengers on that rail line who purchase tickets using a mobile app is $(0.54,\ 0.66)$ . Which interpretation is correct?
A city collected the daily number of emergency-room visits for 45 days. The summary statistics were: mean $= 112$ visits, median $= 105$ visits, standard deviation $= 26$ visits, five-number summary $(60, 92, 105, 125, 210)$ , and IQR $= 33$ visits. Which interpretation is correct?
A company wants to estimate the mean number of sick days taken per employee per year. Two independent simple random samples are drawn from the same employee roster. Sample 1 (n = 30) has a mean of 4.6 sick days; Sample 2 (n = 30) has a mean of 3.8 sick days. Why might the sample results differ?
A school district compares two methods for encouraging homework completion. In a random sample of 180 students using Method A, 126 completed homework every day last week. In a separate random sample of 200 students using Method B, 120 completed homework every day last week. A two-proportion $z$ test was performed for $H_0: p_A=p_B$ versus $H_a: p_A>p_B$ , producing a p-value of 0.002. At the 5% significance level, what conclusion is appropriate?
A university compared mean GPA for students living on campus versus off campus. Using independent random samples, a 97% confidence interval for $(\mu_{\text{on}}-\mu_{\text{off}})$ was $(0.02,\ 0.38)$ . Which interpretation is correct?
A university wants to estimate the mean amount of money spent on textbooks per semester by all undergraduate students. The registrar provides a roster of all undergraduates, and the university uses a random number generator to select 250 students from the roster and emails them a required survey that must be completed to register for next semester. All 250 selected students respond. Which statement best describes the sample representativeness?
A city compares mean commute time (minutes) for residents who use public transit versus residents who drive. The sample mean for transit was 41 minutes and for driving was 37 minutes. A 90% confidence interval for the difference in population means, defined as $\mu_{transit}-\mu_{drive}$ , is $(2, 10)$ . A planner claims, "Public transit users have a longer mean commute time than drivers." Is the claim supported by the confidence interval?
A coffee shop chain wants to test whether a new store layout increases average customer spending. They choose 12 stores that volunteered to try the new layout. The manager flips a coin at each store to randomly assign it to either implement the new layout for one month or keep the current layout for one month, then compares average spending per customer. Which conclusion is justified based on the design?
A nutrition label on a cereal box states that the mean sugar content per serving is no more than 9 grams. A consumer group randomly samples 60 boxes and measures sugar per serving; the sample mean is $\bar{x}=9.4$ grams. Which hypotheses are appropriate for a test of the label's claim about the population mean sugar content $\mu$ ?
The lengths of songs (in minutes) in a large music library are approximately Normal with mean $\mu=3.8$ and standard deviation $\sigma=0.6$ . The normal curve below marks a song length of 2.6 minutes. Which statement about the marked value is correct?
A tech reviewer claims that laptops with solid-state drives (SSD) have a shorter mean boot time than laptops with hard disk drives (HDD). A 98% confidence interval for $(\mu_{\text{SSD}}-\mu_{\text{HDD}})$ is $(-12.5,\ -1.1)$ seconds. Is the claim supported by this interval?
A streaming service sampled 20 users and recorded age ( $x$ , years, from 13 to 62) and average hours streamed per week ( $y$ ). A scatterplot with the least-squares regression line is shown, with fitted equation $\hat{y}=18.0-0.15x$ . The purpose of the linear model is to describe the linear association and predict typical weekly streaming time from age within the observed range. Which interpretation of the model is correct?

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