Practice Test 64 - AP Statistics

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

A city planner recorded the ages (in years) of 52 people who attended a public meeting, based on self-reported age on a sign-in sheet. The dotplot shows the distribution of ages. Which feature of the distribution is most evident?
A discrete random variable $W$ is the number of games a basketball player makes at least one 3-point shot in during a 10-game stretch. The distribution of $W$ has mean $\mu_W=6.7$ and standard deviation $\sigma_W=1.5$ . Which interpretation of the mean is correct?
A website administrator sends an email promotion to 50 randomly selected subscribers. Historically, 18% of subscribers click the link in the email, and each subscriber's decision is assumed independent. Let $X$ be the number of subscribers who click the link (success). Which values correctly model this situation?
A company wants to test whether a new website layout increases the proportion of visitors who make a purchase. Over one week, every visitor to the site is randomly assigned by the server to see either the old layout (control) or the new layout (treatment). The response variable is whether the visitor makes a purchase during that visit. Which statement best describes what random assignment accomplishes in this experiment?
A teacher summarizes quiz scores (out of 20 points) for 30 students. The five-number summary is: min $=4$ , $Q_1=11$ , median $=15$ , $Q_3=17$ , max $=20$ . A standard boxplot is created. Which feature is consistent with the summary statistics?
A nutritionist wants to estimate the mean sodium content (in mg) of a brand of canned soup. She randomly selects 40 cans from that brand's production and measures sodium content. Using a one-sample $t$ interval, she computes a 95% confidence interval of (820 mg, 860 mg) for the population mean sodium content. Which interpretation is correct?
In a large state, the true proportion of households with solar panels is $p=0.12$ . An environmental group repeatedly selects many random samples of size $n=300$ and computes $\hat p$ each time. Which statement about the sampling distribution of $\hat p$ is correct?
To estimate the mean number of hours of sleep per night for all students at a high school, a student researcher posts a link to an online survey on the school's social media page and asks students to report last night's sleep. After two days, 180 students have responded. Which issue most threatens the validity of the results?
A student randomly selects 20 people from a small club of 25 members and records whether each person has paid dues. A success is "paid dues," and exactly 20 members are selected without replacement. Does this meet binomial conditions?
A nutrition study compares the proportion of adults who meet a daily fiber goal in Group S (supplement) versus Group C (control). A 98% confidence interval for $p_S - p_C$ is $(-0.15, -0.01)$ . A researcher claims, "The supplement group has a lower proportion meeting the fiber goal than the control group." Is the claim supported by the confidence interval?
Class X: 10 of 25 prefer A. Class Y: 10 of 100 prefer A. A frequency table shows 10 votes each. Why is it misleading?
A library recorded the number of books checked out per visit for 75 patrons on a weekday. The summaries were: mean = 3.6 books, median = 3 books, SD = 2.2 books, five-number summary = (min 0, $Q_1$ 2, median 3, $Q_3$ 5, max 12), and IQR = 3. Which interpretation is correct?
A phone manufacturer claims its new battery lasts an average of 20 hours under standard testing. A consumer group selects a random sample of $n=25$ batteries and finds a mean lifetime of $\bar{x}=19.2$ hours. They want to test whether the true mean battery life is different from 20 hours. Which hypotheses are appropriate for a test of a population mean?
A city's water department wants to know whether the mean household water pressure differs from the target of $\mu=60$ psi. A random sample of 25 homes is measured, and a one-sample $t$ test is conducted with $H_0:\mu=60$ versus $H_a:\mu\ne 60$ at $\alpha=0.01$ . The p-value is 0.084. What conclusion is appropriate?
A coffee shop claims the mean amount of time customers wait in line during the morning rush is 4 minutes. A manager believes a new ordering system has reduced the mean wait time. After implementation, a random sample of $n=35$ waits has mean $ overline{x}=3.6$ minutes. Which hypotheses are appropriate for testing the manager's claim about the population mean wait time, $\mu$ ?
A battery manufacturer advertises that the mean lifetime of its AA batteries is 10.0 hours. An engineer suspects the true mean lifetime is different from 10.0 hours. A random sample of $n=25$ batteries is tested, and the sample mean lifetime is $\bar{x}=9.6$ hours. Which hypotheses are appropriate for a test of the population mean lifetime, $\mu$ ?
A website records the number of pages viewed, $X$ , during a randomly selected user session. The distribution of $X$ is discrete with mean $\mu_X=9.5$ pages and standard deviation $\sigma_X=3.2$ pages. Which interpretation of the standard deviation is correct?
A manufacturer claims that defects in its products fall into 4 categories with probabilities 0.50 cosmetic, 0.20 packaging, 0.20 functional, and 0.10 missing parts. An auditor inspects 150 defective products and records the observed counts shown in the table. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the claim? Observed counts table (n = 150): Cosmetic 68, Packaging 34, Functional 36, Missing parts 12.
A real estate analyst uses regression to predict house price (in $1000s) from square footage. The analyst claims that each additional square foot increases the predicted price. A 95% confidence interval for the slope is $(-0.02, 0.10)$ thousand dollars per square foot. Is the claim supported by the confidence interval?
Which of the following statements provides the best description of these parameters?

Practice tests