Practice Test 62 - AP Statistics

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

An environmental scientist compares mean nitrate concentration (mg/L) in water from wells near farms versus wells far from farms. Two independent random samples produce a 99% confidence interval for $(\mu_{\text{near}}-\mu_{\text{far}})$ of $(0.05,\ 0.40)$ mg/L. Which interpretation is correct?
An online retailer claims that customers choose shipping options in the following proportions: Standard 60%, Expedited 25%, Overnight 15%. A random sample of 300 orders is selected, and a chi-square goodness-of-fit test is performed at $\alpha=0.01$ . The results are shown below. What conclusion is appropriate? Observed/Expected counts and p-value: - Standard: Observed 165, Expected 180 - Expedited: Observed 90, Expected 75 - Overnight: Observed 45, Expected 45 - p-value = 0.012
A class draws 25 cards with replacement from a well-shuffled standard deck and records color only (Red or Black). The results are Red 13 times and Black 12 times, but the sequence alternates color almost perfectly: R, B, R, B, R, B, ... with only one place where the same color appears twice in a row. Is the pattern consistent with random behavior? Under randomness, you expect some runs; an almost perfectly alternating pattern is possible but may be suspiciously regular.
A candidate's campaign claims that 60% of voters in the district currently support the candidate. A random sample of 500 registered voters finds 280 who say they support the candidate. A one-sample $z$ test for a population proportion is conducted at $\alpha=0.05$ with $H_0:p=0.60$ and $H_a:p<0.60$ . The test produces a $p$ -value of 0.018, so the decision is to reject $H_0$ . Which conclusion is appropriate?
A game designer records the number of attempts players need to beat a level. Let $X$ be the number of attempts for a randomly selected player; $X$ is discrete. The distribution of $X$ has mean $\mu_X=6.5$ attempts and standard deviation $\sigma_X=3.0$ attempts. Which interpretation of the standard deviation is correct?
A botanist compares mean plant height (cm) for seedlings grown under LED light versus fluorescent light. Independent random samples were used (LED: $n=16$ ; Fluorescent: $n=16$ ). A two-sample $t$ test for $\mu_{\text{LED}}-\mu_{\text{Fl}}$ was performed with $H_0:\mu_{\text{LED}}=\mu_{\text{Fl}}$ and $H_a:\mu_{\text{LED}}\ne\mu_{\text{Fl}}$ . The p-value was 0.083. Using $\alpha=0.10$ , what conclusion is appropriate?
A university wants to determine whether intended major is associated with housing type. A random sample of students was taken, and each student was classified by housing (On-campus, Off-campus) and intended major group (STEM, Humanities, Business). A chi-square test of independence was conducted at $\alpha=0.05$ . The observed counts and p-value are shown. What conclusion is appropriate?
A company tests whether a redesigned website changes mean time (in seconds) that visitors spend on a page. A random sample of 60 visitors saw the redesigned page (R) and a separate random sample of 55 visitors saw the original page (O). A two-sample $t$ test for $\mu_R-\mu_O$ is conducted with $H_0: \mu_R-\mu_O=0$ and $H_a: \mu_R-\mu_O\neq 0$ . The p-value is 0.041. Using $\alpha=0.05$ , what conclusion is appropriate?
A store monitors daily revenue from two independent departments. Let $X$ be the revenue (in hundreds of dollars) from electronics with $\mu_X=40$ and $\sigma_X=6$ . Let $Y$ be the revenue (in hundreds of dollars) from clothing with $\mu_Y=25$ and $\sigma_Y=8$ . Define $R=X+Y$ , the total revenue from both departments. Which statement about the combined variable is correct?
In a large school, let $X$ be the number of minutes a randomly selected student spends waiting in the cafeteria line on a randomly selected day. The distribution of $X$ has mean $\mu_X=6.8$ minutes and standard deviation $\sigma_X=2.4$ minutes. Which interpretation of the mean is correct?
A city compares mean monthly electricity use for homes with solar panels (S) versus homes without solar panels (N). A 95% confidence interval for $\mu_S-\mu_N$ is $(-250,\ -60)$ kWh. A resident claims: "Homes with solar panels use less electricity from the grid on average than homes without solar panels." Is the claim supported by the confidence interval?
A streaming service claims that, among its users, time-of-day for starting a movie is distributed as: 20% Morning, 30% Afternoon, 35% Evening, 15% Night. A random sample of 200 movie starts yields: Morning 33, Afternoon 52, Evening 80, Night 35. A chi-square goodness-of-fit test of $H_0$ : the population distribution matches the claim gives $p$ -value = 0.006. Expected counts under $H_0$ are: Morning 40, Afternoon 60, Evening 70, Night 30. What conclusion is appropriate at $\alpha=0.05$ ?
A student uses a random number generator to select 20 lockers (numbered 1–200) to inspect. The selected locker numbers are: 3, 7, 12, 18, 25, 31, 38, 44, 50, 57, 63, 69, 75, 82, 88, 94, 101, 107, 113, 120. Is the pattern consistent with random behavior? Under randomness, selected numbers should not show a clear arithmetic pattern (like steadily increasing by about the same amount).
Which of the following best describes the shape of the probability distribution of X?
A university compares the proportion of students who pass a placement test after taking Course L versus Course M. A 95% confidence interval for the difference in proportions, defined as $p_L - p_M$ , is $(-0.15,\ -0.01)$ . A student claims, "Course L has a lower pass rate than Course M." Is the claim supported by the confidence interval?
A streaming service wants to estimate the proportion of its subscribers who would recommend the service to a friend. It used a random number generator to select 1200 subscriber accounts from its full subscriber list and emailed those accounts a survey; 840 responded, and 72% of respondents said they would recommend the service. The company concluded that "about 72% of all subscribers would recommend the service." Which statement explains whether the conclusion is valid?
A county election office wants to estimate the proportion of registered voters who plan to vote in the next local election. Two polling organizations each take an independent random sample of 500 registered voters from the same county voter file during the same weekend. Poll 1 reports 0.72 plan to vote; Poll 2 reports 0.68 plan to vote. Why might the sample results differ?
A car manufacturer compares the mean fuel efficiency (in miles per gallon) of two tire types. A random sample of 20 cars with Tire Type 1 had a mean of 30.8 mpg, and a random sample of 22 cars with Tire Type 2 had a mean of 29.9 mpg. The research claim is that Tire Type 1 and Tire Type 2 have different population mean fuel efficiencies. Which hypotheses are appropriate for a two-sample $t$ test comparing population means?
A car dealership analyzes whether vehicle age ( $x$ , years) predicts resale price ( $y$ , thousands of dollars) using 60 randomly selected cars. A 90% confidence interval for the population slope is $(-2.7, -1.9)$ thousand dollars per year. Which interpretation is correct?
A school counselor wants to compare the mean number of hours of sleep on school nights for students in two groups: students who participate in a school sport and students who do not. A random sample of 42 athletes had a mean of 7.1 hours, and a random sample of 38 nonathletes had a mean of 6.6 hours. The counselor's research claim is that athletes sleep more on average than nonathletes. Which hypotheses are appropriate for a two-sample $t$ test comparing population means?

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