Practice Test 83 - AP Statistics

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

A call center records the number of calls answered by a randomly selected agent in the first 10 minutes of a shift. Let $X$ be the number of calls, a discrete random variable with mean $\mu_X=4.2$ calls and standard deviation $\sigma_X=1.1$ calls. Which interpretation of the standard deviation is correct?
A nurse attempts to start an IV line and repeats attempts until achieving the first successful insertion. Assume each attempt is independent and the probability of success is constant for this nurse in this setting. The nurse records the number of attempts until the first success. Why is a geometric model appropriate?
A fitness app wants to estimate the mean number of steps per day for all adults in a country. The company analyzes step counts from a random sample of 20,000 current app users and reports the result as the countrywide mean. Which issue most threatens the validity of this conclusion?
A streaming service wants to estimate the proportion of subscribers who watched at least one documentary last week. Two analysts each take an independent simple random sample of 200 subscribers from the same subscriber database and check viewing history. Analyst 1 finds 78 watched a documentary; Analyst 2 finds 92 watched a documentary. Both samples were selected correctly. Why might the sample results differ?
A tech company tests whether a new battery lasts longer than 8 hours on average. The hypotheses are $H_0: \mu = 8$ versus $H_a: \mu > 8$ , using $\alpha = 0.05$ . The company runs the test and rejects $H_0$ , concluding the mean battery life exceeds 8 hours. In reality, the true mean battery life is exactly 8 hours. Which type of error was made?
A school district states that the proportion of its high school students who participate in at least one extracurricular activity is no more than $0.60$ . A random sample of $n=200$ students finds $134$ who participate (sample proportion $\hat{p}=0.670$ ). Which hypotheses are appropriate for testing the district's statement?
A principal wants to estimate the proportion of students at her school who participate in at least one club. She obtains an alphabetized roster of all students and uses a random number generator to select 120 student ID numbers to survey. Which statement best describes the sample representativeness?
A website designer runs a small experiment: for each of 25 visitors shown a new landing page, a success is defined as the visitor clicking the "Sign Up" button. Previous testing suggests the probability of a click is $0.18$ for each visitor (assume independence). Which values of $n$ and $p$ correctly model the number of successes with a binomial distribution?
A botanist models plant height (cm) from amount of fertilizer (grams) for a random sample of plants grown under similar conditions. The botanist claims: "Adding more fertilizer increases mean plant height." A 98% confidence interval for the slope is $(-0.6,\ -0.1)$ cm per gram. Is the claim supported by the confidence interval?
A streaming service recorded whether users have a Premium subscription and whether they primarily watch on a phone or a TV. The two categorical variables are Subscription type (Premium/Basic) and Primary device (Phone/TV). Using the two-way table, which comparison is appropriate for assessing whether subscription type is related to primary device? Which comparison is appropriate?
A university reports that the mean number of credits attempted per semester is $\mu=14.8$ credits for all undergraduates. The distribution of individual credits attempted is discrete and slightly left-skewed. An advisor repeatedly selects random samples of size $n=60$ students and computes $\bar{x}$ . Which statement about the sampling distribution of $\bar{x}$ is correct?
A store manager wants to estimate the population mean amount $\mu$ that customers spend per visit. The manager records the spending amounts for the first 80 customers who enter the store on a Saturday morning and computes the point estimate $\bar{x}$ from those 80 purchases. Which statement describes whether the estimate is biased?
An online retailer claims that at least 90% of orders are shipped within one business day. A random sample of orders will be selected to test this claim. What are the appropriate null and alternative hypotheses?
A jar contains many marbles, each labeled with exactly one letter: {A, B, C}. One marble is drawn at random, the outcome is the letter observed, and the marble is replaced. Let A be the event that the letter is A. Suppose $P(A)=0.50$ . Which statement correctly describes the probability?
A state university wants to know whether students who attend office hours earn higher course grades. Researchers randomly sampled 500 students from all students enrolled in introductory biology and recorded each student's number of office-hour visits and final course grade. Students with more office-hour visits tended to have higher grades. No students were assigned to attend office hours. Which conclusion is justified based on the design of this study?
A political organization wants to estimate the proportion of registered voters in a county who support a ballot measure. Two independent random samples are drawn from the same county voter file. Sample A (n = 500) reports 51% support; Sample B (n = 500) reports 48% support. Why might the sample results differ?
A principal wants to estimate the proportion of students at a large high school who feel safe at school. The principal announces a link to an online survey during morning announcements and posts it on the school's social media, and 1,050 students choose to respond. Which statement best describes the sample representativeness?
A nutrition researcher tests whether adults who follow a Mediterranean-style diet have a lower mean LDL cholesterol level than adults who follow a typical diet. A random sample of 48 Mediterranean-diet adults had a mean LDL of 112 mg/dL, and a random sample of 52 typical-diet adults had a mean LDL of 119 mg/dL. Let $\mu_M$ and $\mu_T$ be the true mean LDL levels for the two diet groups. Which hypotheses are appropriate?
A company measured mean battery life (in hours) for two smartphone models. Using independent random samples, a 90% confidence interval for $(\mu_{A}-\mu_{B})$ was $( -1.6,\ 0.9)$ . Which interpretation is correct?
A farmer models the relationship between fertilizer amount ( $x$ , in kilograms) and crop yield ( $y$ , in bushels) for 32 fields. A 92% confidence interval for the true slope is $(0.8,\ 1.6)$ bushels per kilogram. Which interpretation is correct?

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