Practice Test 44 - AP Statistics

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

A marketing analyst studies whether membership tier is associated with yearly spending. For each of 200 customers (observational units), the analyst records tier coded as 0 = Basic, 1 = Silver, 2 = Gold, 3 = Platinum, and the total dollars spent last year. The goal is to compare spending across tiers. Which classification is correct?
The distribution of diameters (in mm) of ball bearings produced by a factory is approximately Normal for the population of all ball bearings, with mean $\mu=10.00$ mm and standard deviation $\sigma=0.03$ mm. The interval from 9.94 mm to 10.06 mm is marked on the normal curve. Which statement about the marked interval is correct?
A coach compared mean improvement (seconds) in a 100-meter sprint after two different training plans, using independent groups of athletes: Plan P and Plan Q. A 90% confidence interval for $\mu_P-\mu_Q$ is $(0.02,\ 0.15)$ seconds. Which interpretation is correct?
How do the standard deviations of X and Y compare?
A professor claims the mean score on an exam is $\mu=78$ . A random sample of exam scores is used to construct a 90% confidence interval for $\mu$ of $(76,\,80)$ . Is the claim supported by the confidence interval?
A university summarized the number of pages in 55 randomly selected student essays from a large course. The five-number summary was: min $=2$ , $Q_1=4$ , median $=6$ , $Q_3=9$ , max $=18$ . A boxplot is drawn using whiskers to the minimum and maximum. Which feature is consistent with the summary statistics?
A wildlife biologist wants to estimate the average weight of trout in a long river. She marks off the river into 20 equal-length segments, randomly selects 4 segments, and then catches and weighs every trout she can net within those chosen segments during one afternoon. Which statement best describes the sample representativeness?
A city health department tests whether a new text-message reminder system increases the proportion of patients who show up for appointments. They test $H_0: p=0.80$ versus $H_a: p>0.80$ at significance level $\alpha=0.05$ . Based on the sample, they reject $H_0$ and announce that the reminders increase the show-up rate. In truth, the reminder system does not increase the show-up rate (the true proportion is still $p=0.80$ ). Which type of error was made?
A city planner records distance from downtown (miles) and monthly rent (dollars) for apartments. The scatterplot shows a fairly strong negative linear association. Which statement about correlation is correct?
A researcher compares the proportion of commuters who bike to work in two cities. City 1: SRS of $n_1=120$ ; City 2: independent SRS of $n_2=180$ . The statistic is $\hat{p}_1-\hat{p}_2$ . In repeated sampling, the sampling distribution is approximately normal under appropriate conditions and centered at $p_1-p_2$ . Which statement is correct?
A public health official wants to estimate the difference in the proportion of residents who have received a flu shot between two counties. In County A, a random sample of 250 residents finds 160 vaccinated. In County B, a random sample of 220 residents finds 120 vaccinated. Which inference procedure is most appropriate to estimate the difference in proportions?
A relative frequency bar chart was created to show the distribution of blood types (A, B, AB, O) for a random sample of 250 patients. The bar corresponding to Type O blood has a height of 0.44. How many patients in the sample had Type O blood?
A state agency wants to determine whether fewer than 15% of registered voters in the state are unaffiliated with any political party. In a random sample of 800 registered voters, 103 were unaffiliated. A one-sample $z$ test for a population proportion was performed with $H_0: p=0.15$ and $H_a: p<0.15$ at $\alpha=0.05$ . The $p$ -value was 0.041, so the agency rejected $H_0$ . Which conclusion is appropriate?
A quality-control inspector randomly selects 12 light bulbs from a large shipment. Each bulb is tested and classified as either defective or not defective. The company's historical defect rate for this type of bulb is 4%, and the inspector wants to model the number of defective bulbs found in the sample with a binomial distribution. Which values correctly model this situation?
A librarian tracked the number of books checked out by each visitor on a particular day (population: all 60 visitors that day). The five-number summary is: min $=0$ , $Q_1=1$ , median $=2$ , $Q_3=4$ , max $=12$ . A boxplot is drawn. Which feature is consistent with the summary statistics?
A student tracks whether a bus arrives "On time" or "Late" for 20 school days. The student reports the first 10 days were all On time, and the last 10 days were all Late (a sharp switch with no mixing). Under random behavior, you would expect some mixing throughout, though runs can occur; a single abrupt change point can suggest a systematic shift. Is the pattern consistent with random behavior?
A school wants a point estimate of the population mean number of hours of sleep per night, $\mu$ , for all students in the district. Researchers take a simple random sample of 60 students and compute the sample mean $\bar{x}$ . They report $\bar{x}$ as the point estimate for $\mu$ . Which statement describes whether the estimate is biased?
A principal investigates whether grade level is related to how many minutes students spend on homework each night. She surveys 150 students (observational units) and records grade level (9, 10, 11, 12) and minutes of homework on a typical weeknight. The goal is to compare homework time across grades. Which classification is correct?
A manufacturer tests whether the mean breaking strength of a type of rope is greater than 250 pounds. A random sample of 30 ropes is tested, and conditions for a one-sample $t$ test are met. The hypotheses are $H_0: \mu=250$ and $H_a: \mu>250$ at $\alpha=0.01$ . The test is completed and the p-value is 0.009. What conclusion is appropriate?
A genetics lesson states that, for a certain trait in pea plants, each plant has a 25% chance of showing the recessive phenotype. A student grows 12 plants and observes 6 with the recessive phenotype. The student expected about 3 but observed 6. Is the result unexpected, given chance variation with only 12 plants?

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