Practice Test 75 - AP Statistics

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

A website says it shows ads in a random order. A user refreshes the page 30 times and records which ad appears: A appears 18 times, B appears 12 times, with no obvious repeating cycle. Is the pattern consistent with random behavior? Under randomness, you would not expect perfectly equal counts in a small number of trials; some imbalance is typical.
A fitness app wants to estimate the mean number of workouts per week among its active users. Two independent simple random samples are taken from the same set of active users. Sample 1 (n = 100) has a mean of 3.9 workouts/week; Sample 2 (n = 100) has a mean of 4.3 workouts/week. Why might the sample results differ?
A coffee shop tracks the random variable $X$ , the number of customers who enter between 8:00–8:15 a.m. on a randomly selected weekday. The distribution of $X$ has mean $\mu_X=18.0$ customers and standard deviation $\sigma_X=4.5$ customers. Which interpretation of the standard deviation is correct?
A phone manufacturer claims the mean battery life for a certain model is $\mu=18$ hours. From a random sample of users, a 99% confidence interval for $\mu$ is computed as $(17.2,\ 18.9)$ hours. Is the claim supported by the confidence interval?
A nutritionist examines whether systolic blood pressure (mmHg) can be predicted from daily sodium intake (mg). Using a random sample of 55 adults, the nutritionist fits a least-squares regression with blood pressure as the response and sodium intake as the explanatory variable. The nutritionist wants to test whether sodium intake is linearly associated with blood pressure in the population (not specifying direction), so the population slope is not zero. Which hypotheses are appropriate for this slope test?
A botanist measured sunlight exposure in hours per day ( $x$ ) and plant height in centimeters ( $y$ ) for 16 plants of the same species grown in a greenhouse. A least-squares regression of $y$ on $x$ was fit and a slope test was conducted: $H_0: \beta_1=0$ versus $H_a: \beta_1\neq 0$ . The estimated slope was positive with p-value 0.067. Using $\alpha=0.05$ , the botanist wants to interpret the slope test. What conclusion is appropriate?
A teacher wants to estimate the probability that, when 3 students are chosen at random (independently) from a large school where 40% are in 9th grade, at least one of the 3 is a 9th grader. The teacher simulates 10,000 selections by generating 3 random digits 0–9 per trial and letting 0–3 represent "9th grader." The simulation produced 7,844 trials with at least one 9th grader. Which interpretation of the simulation results is correct?
A teacher recorded the number of minutes 35 students spent studying for a quiz the night before, based on a self-reported survey completed the next day. The dotplot below shows the distribution of study times. Which feature of the distribution is most evident?
A school principal believes that fewer than 30% of students arrive late at least once per week. A random sample of 250 students finds that 62 report arriving late at least once per week. A one-sample $z$ test for a population proportion is run at $\alpha=0.10$ with $H_0:p=0.30$ and $H_a:p<0.30$ . The test gives a $p$ -value of 0.041, so the decision is to reject $H_0$ . Which conclusion is appropriate?
A student performs 12 trials of a reaction and records whether a color change occurs within 5 seconds. A success is "color change within 5 seconds," and exactly 12 trials are run, but the chemical concentration decreases each trial, making success less likely. Does this meet binomial conditions?
A card is drawn at random from a standard 52-card deck, and the outcome of interest is whether the card is a heart (H) or not a heart (N), so the sample space is $\{H, N\}$ . The probability of drawing a heart is $P(H)=0.25$ . Which statement correctly describes the probability $0.25$ in this context?
A student is looking at a scatterplot of fuel efficiency (miles per gallon) versus vehicle weight (pounds) for a random sample of 25 car models. The points form a general downward linear trend. Which question addresses the concept of variation that is central to beginning an inference procedure for the slope?
A nonprofit compares the proportion of donors who give again the next year between two outreach strategies. In random samples, 150 of 600 donors contacted with Strategy A gave again, and 196 of 620 donors contacted with Strategy B gave again. A 95% confidence interval for $p_A - p_B$ is $(-0.12,\ -0.01)$ . A director claims that Strategy A results in a higher repeat-donation rate than Strategy B. Is the claim supported by the confidence interval?
A streaming service claims that exactly 25% of its users watch documentaries each week. From a random sample of users, a 99% confidence interval for the population proportion who watch documentaries weekly is $(0.22, 0.28)$ . Is the claim supported by the confidence interval?
The weights of packages shipped by a warehouse are approximately Normal with mean $\mu=12$ lb and standard deviation $\sigma=3$ lb. The normal curve below marks the interval 9 to 15 lb. Which statement about the marked interval is correct?
A school nutritionist wants to compare three types of breakfast (high-protein, high-carb, and balanced) on students' attention scores after first period. Attention may differ by grade level (9th–12th), and the nutritionist can recruit 12 students from each grade. Each student will eat only one breakfast on the test day, and students within a grade can be randomly assigned. Which experimental design is most appropriate?
A national study estimates that 55% of adults exercise at least three times per week. Suppose many random samples of $n=150$ adults are selected, and the sample proportion $\hat p$ is recorded each time. Which statement about the sampling distribution of $\hat p$ is correct?
A scientist examines a scatterplot from a single random sample of data. The points appear to align closely to a straight line with a positive slope. What can the scientist conclude from this plot alone before performing any formal inference?
For all students at a high school, the number of text messages sent per day is approximately Normal with mean $\mu=80$ and standard deviation $\sigma=20$ . The normal curve below marks a value of 40 texts. Which statement about the marked value is correct?
A state transportation agency wanted to estimate the average time (in minutes) that commuters spend waiting for a train during weekday mornings. The agency randomly selected 15 train stations from all stations in the state and then, at each selected station, recorded the waiting time for the first 20 commuters who arrived between 7:00 and 9:00 AM on a single Tuesday. Which conclusion is justified based on the design of this study?

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