Practice Test 59 - AP Statistics

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

An engineer examines whether the thickness of insulation in cm ( $x$ ) predicts heat loss in watts ( $y$ ) from a building. The engineer expects that thicker insulation leads to less heat loss in the population. Which hypotheses are appropriate for testing this expectation about the population regression slope of $y$ on $x$ ?
In a school cafeteria, let $B$ be the number of bananas sold in one day and $A$ be the number of apples sold in one day. Over many days, $\mu_B=120$ with $\sigma_B=15$ , and $\mu_A=80$ with $\sigma_A=12$ . Assume daily banana sales and apple sales are independent. Define the combined variable $T=B+A$ as the total pieces of fruit sold in a day. Which statement about $T$ is correct?
A manufacturer claims its light bulbs last an average of $\mu = 1000$ hours. A consumer group tests a random sample of 25 bulbs and performs a one-sample $t$ test for $H_0: \mu = 1000$ versus $H_a: \mu < 1000$ at $\alpha = 0.05$ . The test produces p-value $p = 0.002$ . Which interpretation of the p-value is correct?
A restaurant chain believes that the proportion of customers who would recommend the restaurant is at least 80%. A random sample of 90 customers is surveyed, and 68 say they would recommend it (so $\hat{p}=0.756$ ). Which hypotheses are appropriate for testing whether the true population proportion $p$ is less than the chain's belief?
A city planner claims that the proportion of drivers who stop completely at a crosswalk is higher after installing a flashing beacon than at similar crosswalks with no beacon. Observers recorded driver behavior at two locations: at the beacon crosswalk, 156 of 300 drivers stopped completely; at the no-beacon crosswalk, 110 of 280 drivers stopped completely. Which hypotheses are appropriate for a test of this claim?
A seed company claims that a particular type of seed germinates with probability 0.85 when planted under standard conditions. A gardener plants 40 seeds, and each seed either germinates or does not germinate; assume independence is reasonable. Let $X$ be the number of seeds that germinate (successes). Which values correctly model this situation?
A nutritionist claims a certain snack has an average sodium content of $\mu=160$ mg per serving. A random sample of 12 servings is tested, and a one-sample $t$ test is performed with $H_0:\mu=160$ and $H_a:\mu<160$ at $\alpha=0.05$ . The p-value is 0.081. What conclusion is appropriate?
A company tested two website layouts and measured the mean time (in seconds) users took to find a product. Layout A users and Layout B users were independent random samples. A 90% confidence interval for $\mu_A-\mu_B$ is $(-6.5,\ -1.0)$ . Which interpretation is correct?
A real estate analyst selects 30 houses in a region and records $x$ = size (hundreds of square feet) and $y$ = selling price (thousands of dollars). The regression of price on size yields a 95% confidence interval for the population slope $\beta$ of $(8,\ 14)$ . Which interpretation is correct?
A city council wants to estimate the mean number of minutes all city residents spend commuting each day. A council member stands outside the downtown subway station from 7:00–8:00 a.m. on Monday and surveys every 5th person who exits the station. Which issue most threatens the validity of using these data to represent all city residents?
A school nutritionist wants to compare three breakfast options (A, B, C) on students' morning alertness scores. Alertness is known to differ by grade level (9th–12th), and the nutritionist can only serve one breakfast to each student on the test day. Within each grade, there are enough volunteers to try all three breakfasts, and students will be tested during the same first-period class. Which experimental design is most appropriate to reduce the effect of grade level while fairly comparing the three breakfasts?
A company tests whether a new training program changes mean weekly sales. A random sample of 42 employees used the new program and a separate random sample of 40 employees used the old program. A two-sample $t$ test for $\mu_{\text{new}}-\mu_{\text{old}}$ was conducted with hypotheses $H_0:\mu_{\text{new}}=\mu_{\text{old}}$ and $H_a:\mu_{\text{new}}\ne\mu_{\text{old}}$ . The test produced a p-value of 0.018. Using $\alpha=0.05$ , what conclusion is appropriate?
A health economist regresses annual medical spending ( $y$ ) on age ( $x$ ) using a random sample of 200 adults. The economist claims there is a negative linear association between age and mean medical spending. A 95% confidence interval for the slope is $(15, 42)$ dollars per year of age. Is the claim supported by the confidence interval?
A hospital compares mean length of stay for patients receiving Treatment A versus Treatment B. They report a 95% confidence interval for $\mu_A-\mu_B$ as $(1.2,\ 3.8)$ days. A doctor claims: "Patients receiving Treatment A stay longer in the hospital on average than those receiving Treatment B." Is the claim supported by the confidence interval?
A university summarized the number of credits earned in the first year by a random sample of 80 first-year students. The summaries were: mean $=28.5$ credits, median $=30$ credits, standard deviation $=4.2$ credits, five-number summary (min $=12$ , $Q_1=26$ , median $=30$ , $Q_3=32$ , max $=36$ ), and IQR $=6$ credits. Which interpretation is correct?
A researcher fits a least-squares regression line to predict weekly study time (hours) from course exam score (points) for a random sample of 40 students. A 95% confidence interval for the population slope is $(0.8, 2.1)$ points per hour. Which interpretation is correct?
A company wants a point estimate of the population proportion $p$ of all customers who would recommend the company. A simple random sample of 200 customers is surveyed, and the sample proportion $\hat{p}$ is computed. The company reports $\hat{p}$ as the point estimate for $p$ . Which statement describes whether the estimate is biased?
A delivery company tracks the number of packages that arrive late to a particular office on a given day. Let the discrete random variable $X$ be the number of late packages on a randomly selected day. The probability distribution of $X$ is shown in the table. Which statement correctly interprets the random variable $X$ ?
A commuter takes a particular train line each morning. For a randomly selected weekday, the train is either On time (O), Delayed (D), or Canceled (C), so the sample space is $\{O, D, C\}$ . Based on several years of records, $P(C)=0.02$ . Which statement correctly describes the probability $0.02$ in this context?
A museum randomly samples 650 visitors to estimate the proportion who would recommend the museum to a friend. The museum wants to claim that at most 70% of all visitors would recommend it (that is, $p\le 0.70$ ). A 90% confidence interval for the population proportion is $(0.68, 0.74)$ . Is the claim supported by the confidence interval?

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