Practice Test 88 - AP Statistics

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

A city planner wants to know whether the distance of a neighborhood from downtown ( $x$ , in miles) predicts the average monthly rent ( $y$ , in dollars). Using data from 45 neighborhoods, the planner fits a least-squares regression of rent on distance. The planner's claim is that rent tends to decrease as distance increases, so the population slope should be negative. Which hypotheses are appropriate for a one-sided test of the population slope?
A school district sampled 30 classrooms and recorded average class size ( $x$ ) and the percent of students meeting a math benchmark ( $y$ ). A linear regression of $y$ on $x$ was fit. The slope was tested using $H_0: \beta_1=0$ versus $H_a: \beta_1\neq 0$ , and the p-value was 0.049 with a negative estimated slope. Using $\alpha=0.05$ , the district wants to interpret the result. What conclusion is appropriate?
A runner compares mean mile time after training with Plan P versus Plan Q. A 90% confidence interval for $\mu_P-\mu_Q$ is $(0.05,\ 0.40)$ minutes, where smaller times are faster. The runner claims: "Plan P produces faster (smaller) mean mile times than Plan Q." Is the claim supported by the confidence interval?
Let $X$ be the discrete random variable representing the number of days in a week that a person exercises. In a large group, the distribution of $X$ has mean $\mu_X=3.9$ days and standard deviation $\sigma_X=1.6$ days. Which interpretation of the mean is correct?
A factory's individual part lifetimes are not normal; the distribution is right-skewed because a few parts last much longer than most. Quality control repeatedly takes random samples of $n=48$ parts and computes the sample mean lifetime $\bar{x}$ . The sampling distribution of $\bar{x}$ is approximately normal. Why is the sampling distribution approximately normal?
A streaming service analyzed a random sample of 250 user accounts and recorded the primary device used to watch content (categorical variable). The bar chart shows counts: Smart TV 110, Phone 68, Laptop 42, Tablet 20, Game console 10. Which statement is supported by the graph?
A school district reports that $30\%$ of all households in the district have no home internet access. A community group suspects the true proportion is lower. In a random sample of $n=160$ households, $38$ report no home internet access (so $\hat{p}=38/160$ ). Which hypotheses are appropriate?
A jar contains many marbles that are either red or blue. Based on a careful count, the probability of drawing a red marble on one random draw (with the marble replaced each time) is $0.60$ . The random process is drawing one marble; the sample space is {red, blue}. Which statement correctly describes the probability $0.60$ ?
A basketball player shoots exactly 20 free throws during practice. A success is making a shot, and a failure is missing. However, the player becomes fatigued, so the chance of making a shot decreases over the 20 attempts. Does this meet binomial conditions?
A manufacturer advertises that only 3% of its light bulbs are defective. A quality-control inspector takes a random sample of 400 bulbs and finds 20 defective. A one-sample proportion test is performed at $\alpha=0.01$ with hypotheses $H_0:p=0.03$ and $H_a:p>0.03$ . The test results in a $p$ -value of 0.004, so the decision is to reject $H_0$ . Which conclusion is appropriate?
A school randomly selects one student ID from a list and records the student's grade level: {9th, 10th, 11th, 12th}. Let S be the event that the selected student is a senior (12th grade). The school reports $P(S)=0.27$ . Which statement correctly describes the probability?
A university randomly sampled 200 students to estimate the proportion $p$ of all university students who have taken at least one online course. In the sample, 124 students had taken an online course. A 90% confidence interval for $p$ is $(0.56,\ 0.68)$ . Which interpretation is correct?
A company investigates the research question: "What proportion of all customers who bought a laptop in the last year are satisfied with their purchase?" The population is all customers who bought a laptop in the last year. The company randomly selects 400 customers from its purchase database and emails them a satisfaction survey; 180 respond, and 85% of those respondents report being satisfied. The company concludes that 85% of all laptop buyers are satisfied. Which statement explains whether the conclusion is valid?
A teacher expects that giving students a 10-minute review game before a quiz will raise the class average from about 75% to about 80%. On a day with the review game, the teacher records quiz scores for 8 randomly selected students: most are in the 70s and 80s, but one student scores 40% after being absent the previous day. The mean of the 8 scores is 73%, slightly below the usual 75%. Is this result unexpected, given variability in quiz performance and the small sample?
A quality inspector selects one item at random from a shipment. Let Event $A$ be "the item is defective," and Event $B$ be "the item is from Machine 1." The inspector is told that $P(A\mid B) > P(A)$ . Which statement about Events $A$ and $B$ is correct?
A website displays an ad repeatedly to a visitor until the visitor clicks the ad for the first time. Assume each display is an independent trial and the probability of a click on any display is constant. The company tracks the number of ad displays until the first click. Why is a geometric model appropriate?
A segmented bar chart is created to show the proportion of students who passed or failed a test, separated by whether they studied more than 5 hours or 5 hours or less. Each bar represents one of the two study time groups. What does the total height of each bar represent?
A teacher asks: "Do students who sit in the front half of the classroom earn higher test scores than students who sit in the back half?" The population is all students in her classes. The plan is to record where each student chooses to sit throughout the unit and then compare test scores for students who usually sit in the front versus the back. Which aspect is most important to address before collecting data?
A student randomly selects one book from a shelf of 60 books. There are 22 fiction books (F), 18 hardcover books (H), and 9 books that are both fiction and hardcover. Let Event A be "the selected book is fiction" and Event B be "the selected book is hardcover." Which statement about Events A and B is correct?
A city engineer tests whether the mean concentration of a contaminant in tap water exceeds the legal limit of 10 ppb. A random sample of 18 water samples is collected, and conditions for a one-sample $t$ test are met. The hypotheses are $H_0: \mu=10$ and $H_a: \mu>10$ at $\alpha=0.10$ . The test is completed and the p-value is 0.121. What conclusion is appropriate?

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