Practice Test 76 - AP Statistics

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

A company wants to compare the distribution of preferred device type for accessing its website across two age groups. A random sample of 120 users ages 18–34 and a separate random sample of 120 users ages 35+ are selected. Each user is classified by preferred device (Phone, Tablet, Computer). The results are shown in a table. Which chi-square test is appropriate, and what are the correct hypotheses? (Multiple groups/samples; one categorical response variable.)
A nonprofit randomly sampled 150 donors to estimate the proportion $p$ of all donors who prefer to be contacted by email rather than phone or mail. In the sample, 87 preferred email. A 95% confidence interval for $p$ is $(0.50,\ 0.66)$ . Which interpretation is correct?
To estimate the population mean commute time $\mu$ for all employees at a large firm, an analyst takes an SRS of 40 employees and records each commute time. She reports the point estimate $\bar{x}+5$ minutes, explaining that people often underreport commute times by about 5 minutes. Which statement describes whether the estimate $\bar{x}+5$ is biased for $\mu$ ?
A city compares mean commute time (minutes) for residents who take the bus versus residents who drive. Two independent random samples were selected (bus: $n=55$ ; drive: $n=50$ ). A two-sample $t$ test for $\mu_{bus}-\mu_{drive}$ used hypotheses $H_0:\mu_{bus}-\mu_{drive}=0$ and $H_a:\mu_{bus}-\mu_{drive}\neq 0$ . The p-value was 0.004. Using $\alpha=0.01$ , what conclusion is appropriate?
A researcher wants to estimate the proportion of all registered voters in a county who approve of a proposed tax. She uses the county voter list and randomly selects 600 voters. However, she only calls during weekday afternoons, and she records opinions from the first 250 people she reaches who answer the phone. Which statement best describes the sample representativeness?
A teacher models exam score ( $y$ ) using number of practice problems completed ( $x$ ). The teacher claims, "Completing more practice problems is associated with higher mean exam scores." A 95% confidence interval for the slope is $(1.4,\ 3.6)$ points per problem. Is the claim supported by the confidence interval?
An online retailer recorded the number of items per order for 80 randomly selected orders placed on one day (from the full set of that day's orders). The dotplot below shows the distribution. Dotplot (items per order): 1 | •••••••••••••••••••••••••• 2 | ••••••••••••••••• 3 | •••••••••• 4 | •••••• 5 | •••• 6 | ••• 7 | •• 8 | • 9 | • 10| • Which feature of the distribution is most evident?
A company tests two website designs and records the proportion of visitors who make a purchase. Design 1 had 96 purchases out of 400 visitors; Design 2 had 88 purchases out of 400 visitors. A 90% confidence interval for $p_1-p_2$ is $(-0.005,\ 0.065)$ . A manager claims Design 1 has a higher purchase rate than Design 2. Is the claim supported by the confidence interval?
A real estate analyst records the size of a house ( $x$ , in square feet) and its selling price ( $y$ , in thousands of dollars) for 40 recently sold homes in a city. The analyst fits a least-squares regression of selling price on size and wants to test whether size is a useful linear predictor of price (i.e., whether there is a nonzero linear association in the population). Which hypotheses are appropriate for a two-sided test of the population slope?
An economist regresses monthly household savings ( $y$ , dollars) on monthly income ( $x$ , dollars). The economist claims, "Higher income is associated with higher mean savings." A 90% confidence interval for the slope is $(0.05,\ 0.22)$ dollars saved per dollar of income. Is the claim supported by the confidence interval?
A health clinic wants to estimate the mean waiting time (in minutes) for walk-in patients on weekdays. Two staff members each independently select a random sample of 30 walk-in patients from the same month and compute the mean waiting time. Staff member 1 gets 18.2 minutes and Staff member 2 gets 21.6 minutes. Assume the month is the same and the sampling method is truly random. Why might the sample results differ?
A sociologist wants to compare the distribution of educational attainment (e.g., high school, bachelor's degree, master's degree) for residents of two different cities. Which graphical display would be most effective for a direct comparison between the two cities?
A student takes two independent quizzes. Let $X$ be the score on Quiz 1 with $\mu_X=78$ and $\sigma_X=6$ . Let $Y$ be the score on Quiz 2 with $\mu_Y=82$ and $\sigma_Y=5$ . Define $A=\frac{X+Y}{2}$ , the average of the two quiz scores. Which statement about the combined variable is correct?
An environmental scientist records, for 22 days, the day's high temperature (x, in °F) and the amount of electricity used in a small office building (y, in kWh). The scientist wants to know whether temperature and electricity use appear to be related. Do the data suggest the variables are related?
An environmental scientist wants to know whether higher daily ozone concentration is associated with higher numbers of asthma-related ER visits. For 45 randomly selected days, the scientist records ozone concentration in ppb (explanatory variable $x$ ) and ER visits (response variable $y$ ) and fits a linear regression predicting visits from ozone. The claim is that as ozone increases, ER visits increase (a positive population slope). Which hypotheses are appropriate for testing this claim about the slope?
Scores on a statewide AP Statistics practice exam for all 11th-grade students in a large district are approximately Normal with mean $\mu=72$ points and standard deviation $\sigma=10$ points. The normal curve below marks a score of 92 points. Which statement about the marked value is correct? (Interpret the marked value in terms of position and spread, not an exact probability.)
A nurse records the systolic blood pressure (mmHg) of a random sample of 52 adults at a clinic. The sample distribution is roughly bell-shaped with slight imperfections but no strong skew or outliers. Why is a normal model reasonable in this situation?
A student randomly selects one number from the set {1, 2, 3, 4, 5, 6}. Let Event A be "the number is prime" and Event B be "the number is even." Which statement about Events A and B is correct?
A company compares delivery times from two warehouses. Many times, it takes an independent random sample of $n_1=25$ deliveries from Warehouse 1 and $n_2=64$ deliveries from Warehouse 2, then computes $\bar{x}_1-\bar{x}_2$ (in minutes). Which statement is correct about the sampling distribution of $\bar{x}_1-\bar{x}_2$ ?
A school district claims the population mean time (in minutes) that students spend on homework per night is $\mu=90$ . A random sample of students is used to construct a 95% confidence interval for $\mu$ : $(84,\ 96)$ . Is the claim supported by the CI?

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