Practice Test 23 - AP Statistics

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

A bag contains 10 marbles: 4 red, 3 blue, and 3 yellow. Two marbles are drawn without replacement. Let Event A be "the first marble is red" and Event B be "the second marble is red." Which statement about Events A and B is correct?
A teacher compared the proportion of students who earned an A on a quiz after two study methods. In a random sample of 90 students using Method 1, 27 earned an A; in a random sample of 85 students using Method 2, 19 earned an A. A two-proportion $z$ test was performed for $H_0: p_1=p_2$ versus $H_a: p_1\ne p_2$ , and the p-value was $0.21$ . At the $\alpha=0.05$ level, what conclusion is appropriate?
A wildlife biologist measured the mass (in grams) of 55 fish caught in a lake. The summary statistics were: mean $= 410$ g, median $= 395$ g, standard deviation $= 120$ g, five-number summary $(150, 320, 395, 470, 920)$ , and IQR $= 150$ g. Which interpretation is correct?
For all manufactured ball bearings from a machine, diameters (in mm) are approximately Normal with mean $\mu=10.00$ and standard deviation $\sigma=0.03$ . A diameter of $x=9.94$ mm is marked. Which statement about the marked value is correct?
A marketing team studies whether the number of advertisements a customer sees in a week ( $x$ ) predicts the amount the customer spends that week ( $y$ , in dollars). They collect data from 50 customers and fit a least-squares regression of spending on ads seen. The team wants to test whether there is evidence of any linear relationship in the population (without specifying direction). Which hypotheses are appropriate for the slope test?
A fitness app company wants to know whether the mean resting heart rate differs between users who follow an "interval training" plan and users who follow a "steady cardio" plan. A random sample of $n=30$ interval users had mean $\bar{x}=64.8$ bpm, and a random sample of $n=28$ steady-cardio users had mean $\bar{x}=67.2$ bpm. The research claim is that the population mean resting heart rates are different for the two plans. Which hypotheses are appropriate?
A school district randomly samples 500 parents to estimate the proportion who favor starting the school day later. The district wants to claim that less than 50% of all parents favor a later start. A 95% confidence interval for the population proportion is $(0.44, 0.49)$ . Is the claim supported by the confidence interval?
A state reports that 57% of drivers have used a hands-free device while driving. Many random samples of $n=1000$ drivers are taken and $\hat p$ is computed each time. Which statement about the sampling distribution is correct?
A city planner claims the population mean commute time for city residents is less than 30 minutes. A random sample of residents is used to create a 99% confidence interval for the mean commute time $\mu$ : $(28.5,\ 31.2)$ . Is the claim supported by the CI?
A nutritionist compares the mean LDL cholesterol level (mg/dL) for adults following a Mediterranean diet versus adults following their usual diet. A sample of $n=32$ Mediterranean-diet adults had a mean LDL of $\bar{x}=112.3$ , and a sample of $n=30$ usual-diet adults had a mean LDL of $\bar{x}=119.7$ . The nutritionist claims the Mediterranean diet reduces the population mean LDL level. Which hypotheses are appropriate?
A physical therapist wants to compare two stretching routines (Routine 1 vs. Routine 2) on flexibility improvement. Flexibility varies widely from person to person, and each patient can complete both routines on separate days one week apart, with the order randomized. The therapist will measure improvement after each routine. Which experimental design is most appropriate to reduce person-to-person variability?
A grocery store tracks the number of items customers buy per trip. The population distribution is not normal: it is discrete and right-skewed, with most customers buying few items and some buying many. A simple random sample of $n=45$ trips is taken, and the mean number of items per trip is calculated. Why is the sampling distribution of the sample mean approximately normal?
Two independent random samples are taken to compare mean commute time (minutes) for employees who work remotely 2 days/week vs employees who never work remotely. A 95% confidence interval for $(\mu_{remote}-\mu_{never})$ is $( -6, -1 )$ . Which interpretation is correct?
At a clinic, let $X$ be the number of phone calls received between 9:00 and 10:00 AM on a randomly selected weekday. The distribution of $X$ has mean $\mu_X=31.4$ calls and standard deviation $\sigma_X=5.6$ calls. Which interpretation of the standard deviation is correct?
A bottling company measures the fill amount in milliliters for a random sample of 60 bottles from one production line. Small variation comes from many tiny sources (machine vibration, temperature, sensor noise), and the distribution appears roughly symmetric with one peak. Why is a normal model reasonable for the fill amounts?
A factory produces metal rods whose lengths are approximately Normal for the population produced today, with mean $\mu=100.0$ cm and standard deviation $\sigma=0.8$ cm. A rod of length 101.6 cm is measured. Which statement about the marked value is correct?
A botanist compares the mean height (in centimeters) of a plant species grown under two light conditions: full sun and partial shade. A random sample of 18 plants grown in full sun had a mean height of 24.6 cm, and a random sample of 17 plants grown in partial shade had a mean height of 22.9 cm. The research claim is that plants grown in full sun have a greater population mean height than plants grown in partial shade. Which hypotheses are appropriate for a two-sample $t$ test comparing population means?
A town wants to estimate the proportion of all registered voters in the town who support a proposed bond measure. The town clerk takes the voter registration list, sorts it alphabetically by last name, and selects every 20th name starting with the first name on the list. The clerk assumes this produces a representative sample. Which issue most threatens the validity of this sampling method?
A clinic categorized 180 patients by whether they received a flu shot and whether they later reported flu symptoms. Under the assumption of independence, which expression calculates the expected count for the Shot & Symptoms cell?
A hospital reports that 80% of patients rate their experience as "satisfied." A researcher repeatedly takes random samples of $n=60$ patients and computes $\hat p$ , the sample proportion satisfied. Which statement about the sampling distribution of $\hat p$ is correct?

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