Practice Test 66 - AP Statistics

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

A student plays 30 rounds of a game and records whether they win each round. A success is "win," and exactly 30 rounds are played. The student's opponent adapts to the student's strategy, making the student less likely to win over time. Does this meet binomial conditions?
An engineer wants to test whether two different machine settings (Setting X vs. Setting Y) affect the strength of a plastic part. Parts are produced on four different machines, and the engineer believes machines may differ slightly in calibration, affecting overall strength. Each machine can produce parts under both settings during the day, and the response is part strength. Which experimental design is most appropriate?
A city planner studies whether distance from downtown ( $x$ , in miles) predicts monthly rent ( $y$ , in dollars) for a random sample of 25 apartments. A slope test is conducted for the regression of rent on distance with $H_0: \beta_1=0$ and $H_a: \beta_1\neq 0$ . The output gives a two-sided p-value of 0.62 for the slope. At the 0.05 level, the planner fails to reject $H_0$ . What conclusion is appropriate?
A retailer compares mean time (in minutes) spent in the store between customers who use a self-checkout app and customers who use traditional checkout. The retailer believes app users spend less time in the store, on average. A random sample of 55 app users had a mean time of 18.3 minutes, and a random sample of 58 traditional-checkout customers had a mean time of 19.6 minutes. Let $\mu_A$ and $\mu_T$ be the true mean times for app and traditional customers. Which hypotheses are appropriate?
A voter advocacy group suspects that the proportion of eligible voters in a county who are registered to vote is less than $0.75$ . A random sample of $n=160$ eligible voters finds $112$ are registered (sample proportion $\hat{p}=0.700$ ). Which hypotheses are appropriate?
A city planner wants to estimate the mean commute time (in minutes) for workers in a city. A random sample of 50 workers is surveyed, and a 95% confidence interval for the population mean commute time is $(28.4, 33.1)$ minutes. Which interpretation is correct?
To compare two products, a store samples customers and records whether each customer makes a purchase. Product A: independent random sample of $n_A=250$ customers; Product B: independent random sample of $n_B=250$ customers. The statistic is $\hat{p}_A-\hat{p}_B$ . Which statement is correct about the effect of independence on the sampling distribution?
A psychologist studies whether a mindfulness app increases average sleep duration. A random sample of 60 app users reported a mean of 7.2 hours/night, while a random sample of 55 nonusers reported a mean of 6.9 hours/night. Let $\mu_A$ be the true mean sleep duration for all app users and $\mu_N$ for all nonusers in the target population. The psychologist's claim is that app users sleep more on average. Which hypotheses are appropriate?
A jar contains only red, blue, and green marbles. One marble is drawn at random. Let event $A$ be "the marble is red" and event $B$ be "the marble is blue." Because the jar contains only these colors, the marble drawn can be exactly one color. Are the two events mutually exclusive?
An ecologist regresses bird species richness ( $y$ ) on park area in hectares ( $x$ ) for 35 parks. The ecologist claims that park area has no linear association with mean species richness (slope $=0$ ). A 95% confidence interval for the slope is $(0.12, 0.88)$ species per hectare. Is the claim supported by the confidence interval?
A card game: from a standard 52-card deck, a player draws 10 cards without replacement and records whether each drawn card is a heart. A success is "heart," and exactly 10 cards are drawn. Does this meet binomial conditions for the number of successes?
A teacher records the number of times a randomly selected student is absent in a 20-day unit. Let $X$ be the absence count, a discrete random variable with distribution: $P(X=0)=0.40$ , $P(X=1)=0.35$ , $P(X=2)=0.15$ , $P(X=3)=0.07$ , $P(X=4)=0.03$ . The mean is $\mu_X=1.02$ absences and the standard deviation is $\sigma_X=1.14$ absences. Which interpretation of the standard deviation is correct?
A delivery app records the number of orders a driver completes in a 4-hour shift. Let $X$ be the number of orders for a randomly selected shift; $X$ is discrete. The distribution of $X$ has mean $\mu_X=14$ orders and standard deviation $\sigma_X=4$ orders. Which interpretation of the mean is correct?
A county election office investigates the research question: "What proportion of registered voters in the county approve of the new voting center location?" The office used a random-digit dialing method that called only landline phone numbers in the county and completed interviews with 520 registered voters; 61% approved. The office concluded that about 61% of all registered voters in the county approve. Which statement explains whether the conclusion is valid?
A museum claims that the long-run distribution of visitor ticket types is 70% adult, 20% child, and 10% senior. On a randomly selected day, a random sample of 300 visitors is taken from that day's visitors, and ticket type is recorded. Observed counts table: Adult 225, Child 54, Senior 21 Claimed distribution: (0.70, 0.20, 0.10). Which hypotheses are appropriate for a chi-square goodness-of-fit test?
A biology lab manual states that 25% of a certain plant's seeds germinate under standard conditions. A student assumes the true germination rate is 25% and tests 80 seeds; 30 germinate (37.5%). The student wants to know whether this outcome is surprising due to random sampling variability with $n=80$ if the true rate is 25%. Is the result unexpected?
A student observes 50 consecutive shots by a player in a game and records whether each shot is made. A success is "made shot," and exactly 50 shots are observed, but the shot difficulty varies greatly (some are layups, some are long 3-pointers). Does this meet binomial conditions?
A student wants to estimate the population mean number of text messages per day, $\mu$ , among students at their school. The student surveys 40 classmates from their own friend group and computes the point estimate $\bar{x}$ from those 40 reported counts. Which statement describes whether the estimate is biased?
A university recorded whether first-year students lived on campus or off campus and whether they joined at least one student club. The two categorical variables are Housing (On campus/Off campus) and Club membership (Joined/Did not join). Based on the two-way table, which comparison is appropriate for assessing whether housing is related to joining a club? Which comparison is appropriate?
A restaurant manager assumes each customer independently leaves a tip of at least 20% with probability 0.55. To estimate the probability that among 8 customers, at least 6 leave a tip of at least 20%, a student simulates 2000 groups of 8 customers (using random digits 0–4 for "no" and 5–9 for "yes"). The simulation produced 612 groups with at least 6 "yes." Which interpretation of the simulation results is correct?

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