Practice Test 24 - AP Statistics

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

Start practice test

1. A company tests whether customer satisfaction ratings differ among three store locations. The company takes independent random samples of customers from each location (Downtown, Mall, Suburb). Each customer rates satisfaction as Low, Medium, or High. The results are shown. Which test is appropriate, and what are the correct hypotheses?
2. A university recorded the ages (in years) of 150 students enrolled in an evening program. The summaries were: mean = 27.8 years, median = 24 years, SD = 8.9 years, five-number summary = (min 18, $Q_1$ 21, median 24, $Q_3$ 30, max 58), and IQR = 9 years. Which interpretation is correct?
3. A restaurant owner compares mean customer wait time (in minutes) on weekends between two staffing plans: Plan A and Plan B. A random sample of 32 weekends using Plan A had a mean wait time of 18.6 minutes, and a random sample of 35 weekends using Plan B had a mean wait time of 17.9 minutes. The research claim is that Plan A results in a longer mean wait time than Plan B. Which hypotheses are appropriate?
4. A museum claims that visitors' favorite exhibit among four options is distributed as follows: 10% Exhibit 1, 20% Exhibit 2, 30% Exhibit 3, and 40% Exhibit 4. A random sample of 150 visitors is surveyed, producing the observed counts below. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the museum's claim?
5. For a pie chart to be a valid display of a categorical variable, the categories must
6. An environmental scientist models daily ozone level (parts per billion) as a linear function of afternoon temperature (°F). From a random sample of 45 summer days, the scientist fits a least-squares regression with ozone level as the response and temperature as the explanatory variable. The scientist's claim is that temperature is linearly related to ozone level (either increasing or decreasing) in the population, so the population slope is not zero. Which hypotheses are appropriate for testing this claim about the slope?
7. A university tests whether students in a flipped classroom have a higher mean final exam score than students in a traditional classroom. A random sample of 45 flipped-class students had a mean score of 81.6, and a random sample of 47 traditional-class students had a mean score of 79.8. Let $\mu_F$ and $\mu_T$ be the true mean final exam scores for flipped and traditional classes, respectively. Which hypotheses are appropriate?
8. For adult men in a country, heights (in inches) are approximately Normal with mean $\mu=70$ and standard deviation $\sigma=3$. An interval is marked: from $x=67$ to $x=73$ inches. Which statement about the marked interval is correct?
9. A psychologist examines the relationship between hours of sleep ($x$) and reaction time ($y$, in milliseconds) for 22 participants. A 95% confidence interval for the true slope is $(-18,\ -2)$ milliseconds per hour. Which interpretation is correct?
10. An economist plots the gross domestic product (GDP) of a country against its adult literacy rate. The points on the scatterplot are very tightly clustered around a straight line with a positive slope. How would the strength of this association be described?
11. A company recorded whether 150 employees work remotely and whether they are in the Sales or Engineering department. Assuming the two variables are independent, which expression calculates the expected count for the Remote & Sales cell?
12. A manufacturer advertises that at least 95% of its light bulbs last 1,000 hours. A quality inspector randomly tested 80 bulbs and found 72 lasted 1,000 hours. A one-proportion $z$ test was conducted for $H_0: p=0.95$ versus $H_a: p<0.95$ at $\alpha=0.05$. The $p$-value was 0.002, so the inspector rejected $H_0$. Which conclusion is appropriate?
13. A delivery company recorded the number of packages delivered per route for 52 routes on a particular day, using the company's route logs. The dotplot below summarizes the distribution. Dotplot (packages per route): 60 | • 65 | •• 70 | ••• 75 | •••• 80 | ••••• 85 | •••••• 90 | ••••••• 95 | •••••• 100| ••••• 105| •••• 110| ••• 115| •• 120| • Which feature of the distribution is most evident?
14. A student randomly selects one book from a shelf. The shelf has 6 fiction books and 4 nonfiction books; among the fiction books, 2 are mysteries. Let Event A be "the selected book is fiction" and Event B be "the selected book is a mystery." Which statement about Events A and B is correct?
15. A die manufacturer claims a six-sided die is fair, so each face (1–6) has probability $\frac{1}{6}$. A student rolls the die 120 times and records the observed counts below. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the manufacturer's claim?
16. A city council member claims that more than 40% of adult residents support building a new public sports complex. A random sample of 250 adult residents is surveyed, and 118 say they support the project (a sample proportion of $\hat{p}=0.472$). Which hypotheses are appropriate for a significance test of the council member's claim about the population proportion $p$?
17. A marketing analyst compares the mean amount spent (in dollars) during a website visit for customers shown a personalized homepage versus customers shown a standard homepage. A sample of $n=60$ personalized-homepage customers had a mean spending of $\bar{x}=42.7$, and a sample of $n=58$ standard-homepage customers had a mean spending of $\bar{x}=40.9$. The analyst claims personalization increases the population mean spending per visit. Which hypotheses are appropriate?
18. A fair die should land on each face with probability $1/6$. A student rolls a die $n=120$ times and records the counts in the table. A chi-square goodness-of-fit test for fairness yields p-value = 0.64. What conclusion is appropriate at the $\alpha=0.05$ level? Observed/Expected counts (with p-value):

    Face	Observed	Expected
    1	18	20
    2	22	20
    3	17	20
    4	21	20
    5	19	20
    6	23	20

    p-value = 0.64
19. A hospital compares two treatments for preventing nausea after surgery. In a sample of 95 patients given Treatment 1, 21 experienced nausea. In a sample of 105 patients given Treatment 2, 34 experienced nausea. The hospital's research claim is that Treatment 1 results in a lower proportion of nausea than Treatment 2. Which hypotheses are appropriate for testing this claim about the population proportions?
20. A county health department wants to estimate the proportion of all adults in the county who have received a flu vaccine this season. They draw a simple random sample from a list of adults who visited any county-run clinic in the past year and call those selected. The department reports the result as the countywide vaccination rate. Which issue most threatens the validity of this sampling plan?

Practice tests