Practice Test 29 - AP Statistics

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

A city planner recorded the ages (in years) of 70 people attending a community meeting by asking each attendee to self-report their age. The dotplot below summarizes the ages. Dotplot (age in years): 18 | •••••••• 19 | ••••• 20 | •••• 21 | ••• 22 | •• 23 | •• 24 | • 25 | • 26 | • 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | • 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | • 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | • Which feature of the distribution is most evident?
A psychologist records number of practice trials ( $x$ ) and reaction time ( $y$ , in milliseconds) for a task. The scatterplot shows reaction time decreasing quickly at first and then approaching a minimum, forming a curve. Which feature suggests a linear model is not appropriate?
A real estate analyst fits a regression model predicting selling price (in thousands of dollars) from square footage for a random sample of homes in a city. The analyst claims: "Larger homes tend to sell for more, on average." A 95% confidence interval for the slope is $(0.0,\ 0.15)$ thousand dollars per square foot. Is the claim supported by the confidence interval?
A fitness app company wants to estimate the proportion of all adults in the U.S. who track their workouts. The company posts a poll on its public social media page and uses the first 5,000 responses as the sample. Which statement best describes the sample representativeness?
To estimate the mean amount of money spent per week on groceries by all households in a county, a researcher interviews shoppers as they leave one large upscale grocery store on Saturday afternoon and asks how much their household spends on groceries in a typical week. Which issue most threatens the validity of generalizing the result to all county households?
A researcher claims that a population of insects has the following genotype distribution: 25% AA, 50% Aa, and 25% aa. A random sample of 200 insects is collected and genotyped; results are shown in a table. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the researcher's claim?
A consumer advocacy group studied the relationship between the sugar content (in grams) and the consumer rating (on a scale of 1 to 100) for a random sample of breakfast cereals. They found a sample slope of -1.5. A primary question for statistical inference would be to determine if this negative slope is:
A nutrition researcher measures daily sugar intake ( $x$ , grams) and fasting blood glucose ( $y$ , mg/dL) for 13 adults. A least-squares regression line is fit to predict fasting glucose from sugar intake: $\hat{y}=84+0.15x$ . The purpose of this linear model is to summarize the association and predict typical fasting glucose for sugar intakes similar to those observed. Which interpretation of the model is correct?
Let $L$ be the number of pages Leah reads on Saturday and $K$ be the number of pages she reads on Sunday. Over many weekends, $\mu_L=40$ with $\sigma_L=9$ , and $\mu_K=55$ with $\sigma_K=12$ . Assume $L$ and $K$ are independent. Define $R=L+K$ , the total pages read over the weekend. Which statement about $R$ is correct?
A materials engineer studies whether increasing the percentage of recycled plastic in a product affects its tensile strength. For 30 production batches, the engineer records recycled content percentage ( $x$ ) and tensile strength in MPa ( $y$ ), then fits a regression model predicting strength from recycled content. The research claim is that recycled content has some linear effect on strength (slope not equal to 0). Which hypotheses are appropriate for testing this claim about the population regression slope?
A nonprofit completed a field experiment to test whether a new donation-letter message increases donations. From its database of 40,000 prior donors, the nonprofit randomly selected 4,000 donors to include in the study. The 4,000 selected donors were then randomly assigned to receive either the standard letter or the new-message letter. The new-message group donated a higher average amount over the next month. Which conclusion is justified based on the design of this study?
In a chi-square test for independence, if the observed count for a particular cell is much larger than its corresponding expected count, what does this suggest?
A company tests two training programs for new employees and measures mean time (in minutes) to complete a standard task after training. From independent random samples, a 99% confidence interval for the difference in population means was computed as $(\mu_{\text{Program 1}}-\mu_{\text{Program 2}})\in(-8.5,\,-2.0)$ . Which interpretation is correct?
A medical screening test is used on a population where, for a randomly selected person, the probability the test returns a false positive is modeled as $P(\text{False positive})=0.02$ . For one test, the sample space is $\{\text{False positive},\text{Not false positive}\}$ , and the event of interest is False positive. Which statement correctly describes the probability $0.02$ ?
A bank models deposits. Let $X$ be the amount (in dollars) deposited on Monday and $Y$ be the amount (in dollars) deposited on Tuesday. Assume $X$ and $Y$ are independent, with $\mu_X=1200$ , $\sigma_X=300$ , $\mu_Y=900$ , and $\sigma_Y=200$ . Define $N=X-Y$ , the net difference (Monday minus Tuesday). Which statement about $N$ is correct?
A health clinic asked 210 patients whether they received a flu shot this season and whether they reported having the flu in the past year. The table summarizes responses. Which comparison is appropriate for evaluating whether flu incidence is associated with receiving a flu shot using conditional distributions? <table> <tr><th></th><th>Had flu</th><th>Did not have flu</th></tr> <tr><td>Flu shot</td><td>24</td><td>96</td></tr> <tr><td>No flu shot</td><td>36</td><td>54</td></tr> </table>
A researcher administers a short survey to randomly selected people walking through a mall until the first person agrees to participate. Each person either "agrees" or "declines," and the researcher stops after the first agreement. Assume the probability a person agrees is approximately constant and each selection is independent. The researcher wants to model the number of people asked until the first agreement. Why is a geometric model appropriate?
A nutrition researcher uses linear regression to predict resting heart rate ( $y$ ) from daily caffeine intake in mg ( $x$ ). The researcher claims the slope is $0$ (no linear relationship). A 95% confidence interval for the slope is $( -0.03,\ 0.11)$ beats per minute per mg. Is the claim supported by the confidence interval?
A fitness coach wants to know whether type of workout is related to change in resting heart rate. She assigns 36 clients to one of three workout plans (cardio, strength, or mixed) and measures each client's resting heart rate at the start and after 8 weeks; she records the change in heart rate (after − before) in beats per minute. The observational units are the clients, and the goal is to compare changes across workout types. Which classification is correct?
A student collects data on 10 phones: battery capacity (mAh) and battery life (hours). The scatterplot shows a positive linear association. Which statement about correlation is correct?

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