Practice Test 2 - AP Statistics

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

What is the value of $P(X \le 2)$ ?
A school district randomly sampled 400 households to estimate the proportion $p$ of all district households that support a proposed tax increase. In the sample, 228 households said they support it. A 95% confidence interval for $p$ was computed as $(0.53,\ 0.61)$ . Which interpretation is correct?
A nutritionist studies whether daily fiber intake ( $x$ , grams) predicts LDL cholesterol ( $y$ , mg/dL) using a random sample of 35 adults. The regression of LDL on fiber is fit, and a slope test is conducted: $H_0: \beta_1=0$ vs. $H_a: \beta_1\neq 0$ . The two-sided p-value is 0.20, so at $\alpha=0.05$ the nutritionist fails to reject $H_0$ . What conclusion is appropriate?
A researcher investigated the relationship between sleep and GPA among high school seniors. The researcher randomly selected 200 seniors from the school roster. Each selected student reported their average hours of sleep per night and their current GPA. The researcher found that students who reported more sleep tended to have higher GPAs. Which conclusion is justified based on the design of this study?
A city library wants to estimate the proportion of adult residents who have a library card. Two different simple random samples were taken from the same city population one week apart. Sample 1 surveyed 120 adults and found 58% had a card, while Sample 2 surveyed 120 adults and found 51% had a card. The sampling method was the same both times, and no major policy change occurred between weeks. Why might the sample results differ?
A standard 52-card deck is thoroughly shuffled, and 1 card is drawn at random. Let event $A$ be "the card is a heart" and event $B$ be "the card is a face card (J, Q, or K)." Are the two events mutually exclusive?
A company surveyed employees about work arrangement (Remote or In-office) and whether they report high job satisfaction (High/Not high). Use conditional distributions to describe the association between work arrangement and job satisfaction. Which comparison is appropriate?
A teacher gives a 10-question multiple-choice quiz where each question has 4 answer choices and exactly one correct answer. A student guesses randomly on every question. Define a success as "the student answers a question correctly," and assume independence across questions. Which values correctly model this situation with a binomial random variable $X$ = number of successes?
Which of the following correctly describes the variables plotted on the axes of a standard residual plot?
A streaming service wants to estimate the proportion of all its subscribers who would recommend the service to a friend. It surveys only subscribers who contacted customer support in the last 30 days, because their email addresses are easy to access, and calculates the recommendation rate from those responses. Which issue most threatens the validity of using this sample to represent all subscribers?
A student checks 70 randomly selected books in a large library and records whether each is currently checked out. A success is "checked out," and exactly 70 books are sampled without replacement. Does this meet binomial conditions?
Researchers want to study whether people who sleep fewer hours tend to have higher stress. They recruit 300 volunteers from a large company by emailing all employees; those who respond complete a survey reporting average sleep hours and a stress score. Which conclusion is justified based on the design? (Assume accurate self-reporting.)
A company tested two website designs to see which leads to more purchases. Among 500 visitors shown Design 1, 62 made a purchase; among 520 visitors shown Design 2, 78 made a purchase. A 99% confidence interval for the difference in purchase rates, $p_1 - p_2$ , is $(-0.05,\ 0.01)$ . Which interpretation is correct?
An environmental scientist took a random sample of 45 water samples from a lake and measured nitrate concentration (in mg/L). A 95% confidence interval for the population mean nitrate concentration was $(3.1, 3.8)$ mg/L. Which interpretation is correct?
A school nurse records the number of days absent for each of 55 students during a semester, using attendance records (whole days). The dotplot shows the distribution. Dotplot of absences (days) 0 | •••••••••••••••••• 1 | •••••••••••• 2 | •••••••• 3 | ••••• 4 | ••• 5 | •• 6 | • 7 | • 8 | • Which feature is most evident?
A manufacturer randomly selects 25 light bulbs from a large shipment and measures their lifetimes (in hours). A one-sample $t$ interval gives a 99% confidence interval for the population mean lifetime of $(980,\ 1045)$ hours. Which interpretation is correct?
A researcher wants to compare four study strategies (flashcards, practice tests, rereading, and summarizing) on a vocabulary test. Students' prior vocabulary level (low vs high, based on a pretest) is expected to strongly affect outcomes. The researcher has 80 students total and can assign each student to only one strategy. Which experimental design is most appropriate?
A grocery store wants to estimate the proportion of customers who use reusable bags. On two different mornings, two employees each take an independent simple random sample of 100 customers from that morning's shoppers (both mornings are typical weekdays). The first sample finds 28% used reusable bags; the second finds 34%. Why might the sample results differ?
A researcher compares mean nightly sleep (in hours) for students who do use a phone in bed vs students who do not. From two independent random samples, a 95% confidence interval for the difference in population means $(\mu_{phone}-\mu_{no\ phone})$ is $(-1.2, -0.3)$ . Which interpretation is correct?
A delivery company defines the discrete random variable $X$ as the number of packages delivered by a randomly selected driver during a randomly selected 30-minute interval. The probability distribution for $X$ is given in the table. Which statement correctly interprets the random variable?

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