Practice Test 87 - AP Statistics

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

Start practice test

1. Two independent random samples are taken to compare mean caffeine intake (mg/day) for adults who drink coffee and adults who do not. The coffee group has $n_1=25$ and the non-coffee group has $n_2=60$. The statistic of interest is $\bar{x}_1-\bar{x}_2$. Over many repetitions, the sampling distribution of $\bar{x}_1-\bar{x}_2$ has mean $\mu_1-\mu_2$ and standard deviation $\sqrt{\sigma_1^2/n_1+\sigma_2^2/n_2}$. Which statement is correct?
2. A quality control manager studies whether machine operating temperature in °C ($x$) predicts the number of defective items produced per hour ($y$). The manager suspects that higher operating temperature increases defects in the population. Which hypotheses are appropriate for testing this claim about the slope in the regression of $y$ on $x$?
3. A weather app states that for this city in early April, the probability that a randomly selected day has measurable rain is $P(\text{Rain})=0.40$. For one day, the sample space is $\{\text{Rain},\text{No rain}\}$, and the event of interest is Rain. Which statement correctly describes the probability $0.40$?
4. The diameters of ball bearings produced by a factory are approximately Normal with mean $\mu=10.00$ mm and standard deviation $\sigma=0.04$ mm. The normal curve below marks the interval 9.92 to 10.08 mm. Which statement about the marked interval is correct?
5. A consumer group wants to answer: "What proportion of residents in our state support a proposed ban on single-use plastic bags?" The population is all adult residents in the state. The plan is to call phone numbers from a list of people who previously signed online environmental petitions and ask whether they support the ban. Which aspect is most important to address before collecting data?
6. A nurse repeatedly checks a patient's blood pressure each hour until the first time the reading falls within a target range. Each hour's reading is classified as either "in range" or "not in range," and the nurse stops once the first "in range" reading occurs. Assume the probability a reading is in range is constant from hour to hour and readings are independent. The nurse wants to model the number of hours checked until the first in-range reading. Why is a geometric model appropriate?
7. A cell has observed count 50, row total 80, column total 60, table total 200. Expected count?
8. A school newspaper wants to estimate the proportion $p$ of all students at the school who support starting classes later. In a random sample of 400 students, 236 said they support a later start time. A 95% confidence interval for $p$ is $(0.545, 0.635)$. Which interpretation is correct?
9. A game app awards a random number of bonus points each time a player opens a daily reward. Let $Y$ be the discrete random variable representing the number of bonus points awarded (0, 5, 10, or 20). The probability distribution of $Y$ is given in the table. Which statement correctly interprets the random variable?
10. A researcher constructs a bar chart showing the number of households with different types of pets (Dog, Cat, Fish, None). If the bars are arranged from tallest to shortest, what is the name of this specific type of bar chart?
11. A teacher claims that students in a large district prefer four types of after-school help in the following proportions: Tutoring 45%, Study Hall 25%, Online Resources 20%, and No Help 10%. The teacher surveys a random sample of $n=150$ students and records the observed counts shown in a table. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the teacher's claim?
12. A jar contains red, blue, and green marbles. One marble is drawn at random. Let Event $A$ be "the marble is red," and Event $B$ be "the marble is blue." Which statement about Events $A$ and $B$ is correct?
13. A streaming service tracks whether a user watches a new-release movie on Friday night. Let event $A$ be "the user watches the new-release movie," and event $B$ be "the user received a push notification about the movie that evening." Data from past weeks suggest users who receive the notification are more likely to watch the movie, so $P(A\mid B)$ is greater than $P(A)$. How does knowing that $B$ occurred affect the likelihood of $A$?
14. The weights (in grams) of all packages of a certain snack are approximately Normal with mean $\mu=250$ and standard deviation $\sigma=8$. A package weight of $x=242$ grams is marked. Which statement about the marked value is correct?
15. Researchers want to determine whether there is an association between smoking status (smoker, nonsmoker) and exercise frequency (0–1 days/week, 2–4 days/week, 5–7 days/week) among adults in a city. They take a random sample of 420 adults and record each person's smoking status and exercise category. Which inference procedure is most appropriate?
16. A city planner sampled 35 intersections and recorded average daily traffic volume in thousands of cars ($x$) and the number of accidents in a year ($y$). A linear regression of $y$ on $x$ was fit. A test of the slope used $H_0: \beta_1=0$ versus $H_a: \beta_1\neq 0$, and the p-value was 0.020 with a positive estimated slope. At the 0.05 level, the planner wants to make a conclusion about linear association. What conclusion is appropriate?
17. A website's page-load times (in seconds) for all visits have mean $\mu=3.2$ and a large standard deviation; the distribution is strongly left-skewed due to a hard lower bound near 0 seconds. A data analyst repeatedly takes random samples of $n=50$ visits and calculates $\bar{x}$ for each sample. Which statement about the sampling distribution of $\bar{x}$ is correct?
18. A poll of 500 randomly selected voters finds that 240 plan to vote for a certain candidate. If the true proportion of voters who support the candidate is 0.5, what is the standard deviation of the number of supporters in a sample of 500?
19. What is the expected count for residents from the North district who are for the park proposal, assuming district and opinion are independent?
20. An online retailer randomly samples 1,200 recent customers to estimate the proportion who are satisfied with their purchase. The retailer wants to claim that more than 85% of all recent customers are satisfied. A 99% confidence interval for the population proportion satisfied is $(0.83, 0.86)$. Is the claim supported by the confidence interval?

Practice tests