Practice Test 52 - AP Statistics

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

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1. When creating a bar chart for the single categorical variable 'Favorite Fruit' with categories Apple, Banana, and Orange, what is a standard convention regarding the bars?
2. A student runs a simulation of 100 trials where each trial results in one of three outcomes: win, lose, or tie. The student defines success as "win," and records the number of wins in 100 trials. Does this meet binomial conditions?
3. A city compares mean commute times for residents who use a new express bus route versus residents who use the regular route. A random sample of $n=52$ express riders had mean $\bar{x}=28.4$ minutes, and a random sample of $n=49$ regular riders had mean $\bar{x}=31.0$ minutes. The claim is that the express route reduces the population mean commute time. Which hypotheses are appropriate?
4. A company that ships packages claims that the mean weight of its "standard" shipment is 12.0 pounds. A random sample of 49 standard shipments is weighed, and the sample mean is $\bar{x}=11.7$ pounds. Which hypotheses are appropriate for testing whether the population mean shipment weight $\mu$ is different from 12.0 pounds?
5. A school counselor wants to know whether students' preferred study location is related to grade level. A random sample of 180 students is selected from the school, and each student reports their grade level (9th, 10th, 11th) and preferred study location (Home, Library). The results are shown in a table. Which chi-square test is appropriate, and what are the correct hypotheses? (One random sample; two categorical variables measured on each individual.)
6. A teacher recorded quiz scores (out of 20 points) for 160 students. The summaries were: mean $=15.2$, median $=16$, SD $=3.1$, five-number summary $(2,\ 14,\ 16,\ 18,\ 20)$, and IQR $=4$. Which interpretation is correct?
7. To test whether background music affects reading comprehension, a researcher randomly selected 120 students from all first-year students at a university. Each selected student was randomly assigned to read a passage either in silence or while listening to instrumental music, then took the same comprehension quiz. The music group scored higher on average. Which conclusion is justified based on the design of this study?
8. A meteorologist recorded daily rainfall amounts (in inches) for 45 days in a spring season at one weather station using a standard rain gauge. The dotplot below shows the distribution. Dotplot (rainfall in inches): 0.0 | ••••••••••••••••••• 0.1 | ••••••••• 0.2 | ••••• 0.3 | ••• 0.4 | •• 0.5 | • 0.6 | • 0.7 | 0.8 | 0.9 | 1.0 | • Which feature of the distribution is most evident?
9. At a large university, the distribution of time (in minutes) it takes students to walk from the main library to the student center is approximately Normal for the population of all such walks. The mean is $\mu=12$ minutes with standard deviation $\sigma=3$ minutes. A particular walk time of 18 minutes is marked on the normal curve. Which statement about the marked value is correct?
10. A school district randomly samples 30 classrooms and estimates the mean number of students per class. A 95% confidence interval for the population mean class size is $(26.4, 29.9)$. A school board member claims the true mean class size is 30 students. Is the claim supported by the confidence interval?
11. A website A/B test assumes that if two page designs are equally effective, each visitor is equally likely to click either design's button, so the probability a visitor clicks Design A is 0.50. In a random sample of 40 visitors shown both designs, 30 click Design A. The team expected about 20 clicks for A but observed 30. Is the result unexpected, given random variation with 40 visitors?
12. A city health department is estimating the mean number of minutes adults in the city exercise per day. Two independent random samples of 80 adults are taken from the same city during the same week. Sample A has a mean of 31.2 minutes; Sample B has a mean of 27.9 minutes. Why might the sample results differ?
13. A city health department investigates the research question: "Is the mean number of hours of sleep for adults in the city at least 7 hours?" Interviewers stood outside a downtown gym on weekday mornings and surveyed 85 adults leaving the gym; the sample mean was 7.4 hours. The department concluded that adults in the city average at least 7 hours of sleep. Which statement explains whether the conclusion is valid?
14. A biologist tags 9 turtles and later checks whether each tagged turtle is recaptured during a follow-up survey. Assume each turtle's recapture status is independent of the others and the probability a tagged turtle is recaptured is $0.30$. Let $X$ be the number of tagged turtles recaptured. Which values correctly model this situation with a binomial distribution (identify $n$ and $p$)?
15. A hospital screens 35 patients for a particular infection using a rapid test. A success is defined as a positive test result. For this group, the probability a patient tests positive is 0.08, and patient results are treated as independent. If $X$ is the number of positive test results, which values correctly model this situation (identify $n$ and $p$)?
16. A student rolls two dice 30 times and records whether the sum is 7. A success is "sum equals 7," and exactly 30 rolls are made. Does this meet binomial conditions for the number of successes?
17. A real estate analyst wants to know whether larger houses tend to sell for more. From a random sample of 50 recent sales in a city, the analyst records living area in square feet ($x$) and sale price in thousands of dollars ($y$) and fits a regression line predicting price from area. The research claim is that the relationship is linear with a positive slope. Which hypotheses are appropriate for testing this claim about the population regression slope?
18. A consumer group compared the proportion of defective items produced by two factories. In a random sample of 500 items from Factory A, 34 were defective; in a random sample of 450 items from Factory B, 18 were defective. A two-proportion $z$ test was conducted for $H_0: p_A=p_B$ versus $H_a: p_A>p_B$, and the p-value was $0.004$. Using $\alpha=0.05$, what conclusion is appropriate?
19. A researcher completed an experiment to test whether a brief mindfulness exercise reduces test anxiety. At one high school, 10 math classes were available. The researcher randomly assigned 5 entire classes to do a 5-minute mindfulness exercise before a unit test and the other 5 classes to follow the usual pre-test routine. All students then took the same unit test and completed an anxiety scale immediately beforehand; the mindfulness classes reported lower average anxiety. Which conclusion is justified based on the design of this study?
20. A school nurse records the resting heart rates (beats per minute) of a simple random sample of $n=60$ students during homeroom to estimate the typical resting heart rate at the school. The nurse plans to use a normal model to describe the distribution of resting heart rates in the student population. Why is a normal model reasonable in this situation?

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