Practice Test 72 - AP Statistics

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

A hospital summarized the waiting time (in minutes) for 75 patients in an urgent care clinic. The summaries were: mean $=58.0$ , median $=49.0$ , SD $=30.0$ , $Q_1=32.0$ , $Q_3=70.0$ , minimum $=8$ , maximum $=160$ (five-number summary: $8, 32, 49, 70, 160$ ). Which interpretation is correct?
An environmental scientist compares mean nitrate concentration (in mg/L) in groundwater near farms that use a new fertilizer formulation versus farms that use the standard formulation. A random sample of $n=14$ wells near new-formulation farms had a mean of $\bar{x}=7.8$ mg/L, and a random sample of $n=13$ wells near standard-formulation farms had a mean of $\bar{x}=8.5$ mg/L. The scientist claims the new formulation lowers the population mean nitrate concentration. Which hypotheses are appropriate?
A real estate analyst collected data from $n=22$ homes on size ( $x$ , in square feet) and sale price ( $y$ , in thousands of dollars). The least-squares regression of price on size produced slope $b_1=0.19$ . The analyst tested $H_0: \beta_1=0$ versus $H_a: \beta_1>0$ and obtained a p-value of $0.047$ . Using this completed slope test at $\alpha=0.05$ , what conclusion is appropriate?
A university states that 25% of its students participate in intramural sports. A random sample of 300 students finds that 90 participate. A one-sample proportion test is run at $\alpha=0.05$ with $H_0:p=0.25$ and $H_a:p\ne 0.25$ . The test gives a $p$ -value of 0.39, so the decision is to fail to reject $H_0$ . Which conclusion is appropriate?
What is the probability that a randomly selected person has more than 1 but at most 3 successful attempts?
Individual restaurant tip percentages are not normally distributed; they are slightly right-skewed with occasional very large tips. A researcher repeatedly selects random samples of $n=30$ receipts and computes the sample mean tip percentage $\bar{x}$ . The sampling distribution of $\bar{x}$ is approximately normal. Why is the sampling distribution approximately normal?
A researcher compares the proportion of defective parts produced by two machines. From independent random samples, Machine M had 18 defectives out of 300 parts, and Machine N had 9 defectives out of 300 parts. A two-proportion $z$ test for $H_0: p_M-p_N=0$ versus $H_a: p_M-p_N>0$ yielded a p-value of $0.03$ . At $\alpha=0.05$ , what conclusion is appropriate?
To compare two fertilizers, a researcher repeatedly takes an independent random sample of $n_1=10$ plants grown with Fertilizer A and $n_2=10$ plants grown with Fertilizer B, then records the mean height for each sample and computes $\bar{x}_A-\bar{x}_B$ . Suppose the population of heights for each fertilizer is strongly right-skewed, with no extreme outliers. Which statement is correct about the sampling distribution of $\bar{x}_A-\bar{x}_B$ ?
A website tracks the number of items a customer places in their cart per visit. Let $X$ be the number of items for a randomly selected visit; $X$ is discrete. The distribution of $X$ has mean $\mu_X=4.0$ items and standard deviation $\sigma_X=2.5$ items. Which interpretation of the standard deviation is correct?
A city planner compares distance from downtown (x, in miles) to average apartment rent (y, in dollars) for 15 neighborhoods. The scatterplot shows rent dropping steeply near downtown and then flattening farther out. Which feature suggests a linear model is not appropriate for predicting rent from distance?
Two pain relievers are compared by measuring mean time (minutes) until relief. Drug A had a sample mean time of 24 minutes and Drug B had 28 minutes. A 95% confidence interval for the difference in population means, defined as $\mu_A-\mu_B$ , is $(-8, -1)$ . A doctor claims, "Drug A provides relief faster on average than Drug B." Is the claim supported by the confidence interval?
A city planner records the commute times (in minutes) for 45 randomly selected workers who drive to downtown. The five-number summary is: min $=12$ , $Q_1=18$ , median $=26$ , $Q_3=41$ , max $=58$ . A boxplot is constructed. Which feature is consistent with the summary statistics?
A researcher tests whether the mean daily screen time for students at a college is greater than 5 hours. A random sample of 60 students is taken, and a one-sample $t$ test is conducted with $H_0: \mu = 5$ hours and $H_a: \mu > 5$ hours at $\alpha=0.01$ . The p-value is 0.02. What conclusion is appropriate?
A city planner models the relationship between distance from downtown ( $x$ , in miles) and monthly rent ( $y$ , in dollars) using data from 40 apartments. A 90% confidence interval for the true slope is $(-85,\ -20)$ dollars per mile. Which interpretation is correct?
A manufacturer wants a point estimate of the population mean lifetime $\mu$ (in hours) of a certain type of lightbulb. To construct the estimate quickly, an engineer tests 25 bulbs from a batch that passed an initial quality screen and computes the sample mean lifetime $\bar x$ , reporting $\bar x$ as the point estimate for $\mu$ for all bulbs produced. Which statement describes whether the estimate is biased?
A grocery store manager claims that more than 10% of customers use reusable bags. A random sample of 120 customers finds 9 who use reusable bags ( $\hat{p}=0.075$ ). Which hypotheses are appropriate for testing the manager's claim with a one-proportion test?
A nonprofit wants to estimate the proportion $p$ of residents in a region who have volunteered at least once in the past year. In a random sample of 360 residents, 99 report volunteering. A 95% confidence interval for $p$ is $(0.23, 0.32)$ . Which interpretation is correct?
A biologist observes a nest over exactly 12 feeding visits by a parent bird. On each visit, the food delivered is classified as insect, worm, or seed. The biologist records how many visits involved insects. Does this meet the binomial conditions for counting insect visits as successes?
A public health official wants to estimate the mean number of servings of vegetables eaten per day by adults in a county. A random sample of 100 adults was surveyed, and a 97% confidence interval for the population mean was reported as $(2.1,\ 2.8)$ servings. Which interpretation is correct?
A school district compared the mean number of minutes of homework completed per night for students using a new study app versus students not using the app. From independent random samples, a 95% confidence interval for the difference in population means $(\mu_{\text{app}}-\mu_{\text{no app}})$ was computed as $(4.2,\ 11.8)$ minutes. Which interpretation is correct?

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