Practice Test 46 - AP Statistics

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

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1. Which value in this dataset is best described as a potential outlier?
2. A student's total time spent on homework in a week is modeled by two independent random variables. Let $X$ be time (in hours) spent on math homework with $\mu_X=5$ and $\sigma_X=1.5$. Let $Y$ be time (in hours) spent on English homework with $\mu_Y=3$ and $\sigma_Y=1.0$. Define $S=X+Y$, the total time on math and English homework. Which statement about the combined variable is correct?
3. A jar contains 200 beads, 40 of which are red. A student randomly draws 20 beads with replacement and records whether each bead is red. A success is "red," and exactly 20 draws are made. Does this meet binomial conditions?
4. A city transit agency reports that the mean wait time for a bus on a certain route is 12 minutes. A commuter advocacy group randomly samples $n=35$ bus arrivals and records wait times, obtaining a sample mean of $\bar{x}=13.1$ minutes. The group wants to test whether the true mean wait time is different from 12 minutes. Which hypotheses are appropriate?
5. Let $F$ be the amount of time (in hours) a phone battery lasts after a full charge with Feature A turned on, and let $G$ be the amount of time (in hours) it lasts with Feature A turned off, for randomly selected days. Over many days, $\mu_F=9.5$ with $\sigma_F=1.1$, and $\mu_G=11.0$ with $\sigma_G=1.4$. Assume $F$ and $G$ are independent across days. Define $H=G-F$, the increase in battery life when the feature is off. Which statement about $H$ is correct?
6. A marketing team is studying which social media platform customers most associate with a brand. From the population of customers who follow the brand online, a random sample of 140 customers is surveyed, and each customer selects the platform they most associate with the brand (a categorical variable). The distribution is shown below. Which statement is supported by the data?

   Platform most associated with the brand	Frequency	Relative frequency
   Instagram	56	0.400
   TikTok	42	0.300
   YouTube	28	0.200
   Facebook	14	0.100

7. A manufacturer compares the mean lifetime of batteries from two production lines. In repeated sampling, an independent random sample of $n_1=16$ batteries from Line 1 and $n_2=16$ batteries from Line 2 is tested, and $\bar{x}_1-\bar{x}_2$ is recorded. Which statement is correct about how the standard deviation of the sampling distribution changes if both sample sizes are quadrupled (to $n_1=n_2=64$)?
8. A farmer records the weights (in pounds) of 35 pumpkins harvested from one field. The five-number summary is: min $=4.8$, $Q_1=7.2$, median $=9.0$, $Q_3=11.5$, max $=18.6$. A standard boxplot is drawn. Which feature is consistent with the summary statistics?
9. A school district compares mean number of absences in a semester for students who start school at 8:00 a.m. versus students who start at 9:00 a.m. A random sample of 40 students with an 8:00 start had a mean of 6.1 absences, and a random sample of 42 students with a 9:00 start had a mean of 5.4 absences. The district's claim is that the mean number of absences differs between the two start times. Which hypotheses are appropriate?
10. A teacher studies whether the number of practice problems completed ($x$) predicts score on a quiz ($y$). The teacher claims that completing more practice problems increases quiz scores in the population. Which hypotheses are appropriate for testing this claim about the slope in the regression of $y$ on $x$?
11. A fitness coach compares mean change in resting heart rate (in beats per minute) after 8 weeks for two workout plans: Plan X and Plan Y. A random sample of 20 clients on Plan X had a mean change of −4.1 bpm, and a random sample of 22 clients on Plan Y had a mean change of −2.7 bpm. The research claim is that the mean change differs between the two plans. Which hypotheses are appropriate?
12. An ecologist claims that a certain species of beetle has four color morphs occurring in proportions 0.10, 0.20, 0.30, and 0.40. A random sample of 200 beetles is captured and each beetle is classified into one of the four morph categories (categorical). Which inference procedure is most appropriate to test whether the observed counts are consistent with the claimed distribution?
13. An online retailer studies the amount spent per order. The population distribution is strongly right-skewed because most orders are small but a few are very large. The analyst repeatedly takes random samples of $n=100$ orders and computes the sample mean amount spent $\bar{x}$. She examines the sampling distribution of $\bar{x}$. Why is the sampling distribution approximately normal?
14. A school district wants to estimate the proportion of all parents in the district who are satisfied with remote learning options. The district posted a survey link on its website and social media accounts and received 1200 responses; 68% reported being satisfied. The district concluded that "about 68% of all parents in the district are satisfied with remote learning options." Which statement explains whether the conclusion is valid?
15. A school compares two study programs by repeatedly taking random samples of students from each program. Each time, a random sample of $n_1=40$ students from Program A and an independent random sample of $n_2=40$ students from Program B are selected, and the mean exam score is computed for each group. The statistic of interest is $\bar{x}_A-\bar{x}_B$. Which statement is correct about the sampling distribution of $\bar{x}_A-\bar{x}_B$?​
16. A basketball player makes 70% of free throws in the long run. During one practice, she shoots 20 free throws and makes 10. She expected about 14 makes but observed 10. Is the result unexpected, given natural variability in 20 shots?
17. A state health department wants to estimate the mean number of hours of exercise per week for all adults in the state. The department divides the state into urban and rural counties, then randomly selects 50 adults from urban counties and 50 adults from rural counties using voter registration lists. Which statement best describes the sample representativeness?
18. A university estimates that 50% of applicants submit test scores. A counselor repeatedly takes many random samples of $n=200$ applicants and computes $\hat p$. Which statement about the sampling distribution is correct?
19. A manufacturer advertises that 90% of its light bulbs last at least 1,000 hours. A quality-control team randomly tests 80 bulbs and finds that 66 last at least 1,000 hours. A one-sample $z$ test for a population proportion was conducted with $H_0: p=0.90$ versus $H_a: p<0.90$ at significance level $\alpha=0.05$. The test produced a $p$-value of 0.012, so the null hypothesis was rejected. Which conclusion is appropriate?
20. A study categorized 90 commuters by whether they bike to work and whether their commute is under 5 miles or 5 miles and over. Assuming independence, which expression calculates the expected count for the Bike & Under 5 miles cell?

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