Practice Test 95 - AP Statistics

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

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1. A school district wants to know whether preferred after-school activity is associated with grade level. A random sample of students was selected, and each student reported one preferred activity. A chi-square test of independence was performed at the $\alpha=0.05$ level. The two-way table of observed counts and the computer output p-value are shown. What conclusion is appropriate?
2. What is the most likely statistical explanation for this observed positive association?
3. A farmer measures the weight (in pounds) of individual apples from a large orchard. The population mean is $\mu=0.35$ lb with population standard deviation $\sigma=0.08$ lb, and the population distribution is not known. Each week, the farmer repeatedly takes random samples of size $n=16$ apples and calculates the sample mean weight $\bar{x}$. Which statement about the sampling distribution of $\bar{x}$ is correct?
4. A city transit app notes whether a rider checks real-time arrival updates before leaving (event $A$) and whether the rider arrives late to work (event $L$). Riders who check updates might avoid delays, so lateness may be less common among them. How does knowing that a rider checked real-time updates ($A$ occurred) affect the likelihood that the rider arrived late ($L$)?
5. A bookstore tracks $X$, the number of items purchased in a randomly selected transaction. The distribution of $X$ has mean $\mu_X=2.4$ items and standard deviation $\sigma_X=1.1$ items. Which interpretation of the standard deviation is correct?
6. A psychologist administers a standardized reaction-time task to a random sample of 50 adults and records each person's reaction time (in milliseconds). The psychologist wants a model to describe typical reaction times and the chance of unusually slow responses. Why is a normal model reasonable?
7. A city council member claims that more than 60% of residents support a proposed public transit expansion. A random sample of 500 residents is surveyed, and a 95% confidence interval for the true population proportion who support the expansion is $(0.57, 0.63)$. Is the claim supported by the confidence interval?
8. A city planner studies the daily number of pothole complaints. The population distribution is highly right-skewed: most days have few complaints, but some days have many. She repeatedly selects random samples of $n=75$ days and computes the sample mean number of complaints $\bar{x}$. She considers the sampling distribution of $\bar{x}$. Why is the sampling distribution approximately normal?
9. An environmental agency samples 30 water sites in a river and estimates the mean concentration of a pollutant to decide whether to issue a "do not drink" advisory. Issuing an advisory can cause economic harm, but failing to issue one could put residents at risk. Why is it important to consider potential error when using the sample estimate to make this decision?
10. A school counselor wants to learn whether an optional after-school tutoring program is associated with higher Algebra 1 exam scores. The counselor compares exam scores for all 86 ninth-graders who chose to attend tutoring at least once (mean $=82$) and all 190 ninth-graders who did not attend (mean $=76$) at one high school this semester. Which conclusion is supported by the data?
11. A student records the number of text messages they receive in a 10-minute interval. Let $X$ be the number of texts received in a randomly selected 10-minute interval. The probability distribution of $X$ is shown in a table. Which statement correctly interprets the random variable $X$?
12. A school administrator samples $n=60$ students and fits a least-squares regression model predicting final exam score ($y$, points) from number of absences ($x$). The administrator's claim is that, in the population, absences are associated with lower exam scores (negative slope). Which hypotheses are appropriate for testing this claim about the population slope?
13. Which of the following best describes the two variables of interest for this study?
14. A card is drawn 15 times without replacement from a standard 52-card deck. A success is drawing a heart, and a failure is drawing a non-heart. A student wants to use a binomial model for the number of hearts drawn in 15 draws. Does this meet binomial conditions?
15. A student's daily screen time is modeled with two independent random variables: $X$, minutes on social media with $\mu_X=80$ and $\sigma_X=20$, and $Y$, minutes watching videos with $\mu_Y=50$ and $\sigma_Y=15$. Define $T=X+Y$ as total screen time. Which statement about $T$ is correct?
16. A company tested two package designs (Design A vs Design B) and recorded whether customers said they would buy the product (Yes/No). The purpose is to compare the conditional proportions of "Yes" between designs. Based on the two-way table, which comparison is supported? Two-way table of Design by Response (proportions of all customers): - A & Yes: 0.30, A & No: 0.20 - B & Yes: 0.25, B & No: 0.25
17. A school district wants to estimate the proportion of all parents of students in the district who support changing the start time. The district emailed a survey link to every parent on file and reported results based only on the 18% who completed the survey within 48 hours. Which issue most threatens the validity of using this sample to generalize to all parents in the district?
18. A psychologist compares mean reaction time (milliseconds) for participants after drinking caffeinated coffee versus decaf. Two independent random samples yield a 98% confidence interval for $(\mu_{\text{caff}}-\mu_{\text{decaf}})$ of $(-30,\ -5)$ ms. Which interpretation is correct?
19. A delivery company tracks package weights. Let $X$ be the weight (in pounds) of a randomly selected package from Warehouse A with $\mu_X=12$ and $\sigma_X=4$. Let $Y$ be the weight (in pounds) of a randomly selected package from Warehouse B with $\mu_Y=9$ and $\sigma_Y=5$. Assume $X$ and $Y$ are independent. Define $D=X-Y$, the difference in weights (A minus B). Which statement about the combined variable is correct?
20. What is the value of k?

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