Practice Test 70 - AP Statistics

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

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1. A wildlife researcher expects a certain bird species to choose nesting sites in 3 habitat types in the proportions 0.50 forest, 0.30 grassland, 0.20 wetland. In a random sample of 90 nests, the researcher records the habitat type and performs a chi-square goodness-of-fit test of $H_0$: the population proportions match 0.50/0.30/0.20 versus $H_a$: they do not. The p-value is 0.72. The observed and expected counts are shown. What conclusion is appropriate at the $\alpha=0.05$ level?
2. A city planner wants to test whether average monthly electricity use differs between apartments with smart thermostats and apartments without smart thermostats. A random sample of 35 smart-thermostat apartments had a mean of 410 kWh/month, and a random sample of 40 non-smart apartments had a mean of 435 kWh/month. Let $\mu_S$ be the true mean monthly electricity use for all smart-thermostat apartments in the city and $\mu_N$ for all non-smart apartments. Which hypotheses are appropriate?
3. A public health team completed an observational study about sleep and blood pressure. They recruited 600 adult volunteers who responded to an online advertisement and recorded each person's average hours of sleep per night and resting systolic blood pressure during one clinic visit. The team found that adults who reported fewer hours of sleep tended to have higher blood pressure. Which conclusion is justified based on the design of this study?
4. A lab measures the difference (in grams) between the target mass and the actual mass for 70 samples prepared on the same scale. Errors arise from many tiny sources (air currents, rounding, instrument noise) and are centered near 0 with a roughly symmetric, single-peaked shape. Why is a normal model reasonable for these measurement errors?
5. To compare the favorite type of movie (Action, Comedy, Drama, Sci-Fi) for samples of high school students and middle school students, a segmented bar chart is created. If the sample sizes for the two groups are different, which type of scaling on the vertical axis is most appropriate for a fair comparison?
6. A manufacturer reports that the lifetimes (in hours) of a certain type of light bulb are approximately Normal for the population of all bulbs produced, with mean $\mu=800$ hours and standard deviation $\sigma=50$ hours. The value 850 hours is marked on the normal curve. Which statement about the marked value is correct?
7. A bookstore manager wants to understand customer preferences. Over one weekend, the manager asked 150 customers (not randomly selected) which genre they were primarily shopping for (categorical variable). The bar chart shows counts: Fiction 52, Mystery 31, Nonfiction 29, Fantasy 24, Poetry 14. Which statement is supported by the graph?
8. A school district wants to compare whether the distribution of preferred after-school activity (Sports, Clubs, Homework help) is the same for students from three different schools. A random sample of students is selected from each school, and each student reports one preferred activity. The results are summarized below. Which test is appropriate, and what are the correct hypotheses?
9. A restaurant chain wants to estimate the average amount spent per visit by all customers nationwide. Managers at 15 locations are asked to "collect receipts from the next 40 customers you see," and they send those receipts to headquarters. Headquarters computes the mean spending from the collected receipts. Which issue most threatens the validity of this sampling plan?
10. A researcher compares the proportion of defective items from two manufacturing lines. Line A: 18 defectives out of 300; Line B: 30 defectives out of 300. A 95% confidence interval for $p_A-p_B$ is $(-0.08,\ -0.01)$. The researcher claims the defect rate is lower on Line A than on Line B. Is the claim supported by the confidence interval?
11. A city wants to estimate the mean number of minutes residents spend commuting to work. The city obtains a list of all residential addresses and uses a random number generator to select 800 addresses; a survey is mailed to each selected household and 210 households return completed surveys. Which statement best describes the sample representativeness?
12. A school district surveyed a simple random sample of 200 students from its 4 high schools about whether they usually eat breakfast on school days. In the sample, 118 students said "yes." Which conclusion is supported by these data?
13. An agricultural scientist compares three fertilizers on tomato yield. The explanatory variable is fertilizer type (F1, F2, F3), and the response variable is total tomato mass harvested per plant. The scientist has 30 similar plants in a greenhouse and assigns 10 plants at random to each fertilizer. Which feature of this design is an example of replication?
14. A fitness app claims the population mean number of steps its users take per day is $\mu=10{,}000$. From a random sample of users, a 95% confidence interval for $\mu$ is computed as $(9{,}700,\ 10{,}400)$. Is the claim supported by the CI?
15. A wildlife biologist measures the mass (in kilograms) of 52 adult turtles in a pond. The five-number summary is: minimum $3.1$, $Q_1=4.0$, median $4.6$, $Q_3=5.8$, maximum $9.2$. A boxplot is drawn from these values (no outliers shown). Which feature is consistent with the summary statistics?
16. A city compared mean commute times for two independent groups: commuters who use public transit (T) and commuters who drive (D). A 92% confidence interval for $\mu_T-\mu_D$ is $(3,\ 11)$ minutes. Which interpretation is correct?
17. A city's transit authority estimates that the probability a randomly selected bus arrives within 2 minutes of its scheduled time is $0.65$. Consider the random process of selecting one bus arrival at random; the sample space is {within 2 minutes, not within 2 minutes}. Which statement correctly describes the probability $0.65$?
18. A restaurant chain wants to know whether menu preference differs by region. A random sample of customers from each region (East, Midwest, West) is asked to choose their favorite entree (Chicken, Beef, Vegetarian). The results are below. A chi-square test of homogeneity gives $p=0.20$. What conclusion is appropriate at the $\alpha=0.05$ level? Two-way table (counts):

    Region	Chicken	Beef	Vegetarian
    East	52	44	24
    Midwest	48	50	22
    West	55	40	25

19. Which of the following is the most accurate statement based on this residual?
20. A restaurant owner claims that the long-run distribution of entrée orders during dinner is 50% pasta, 20% burger, 15% salad, and 15% tacos. Over a randomly selected set of 180 dinner orders, the counts are recorded. Observed counts table: Pasta 84, Burger 44, Salad 22, Tacos 30 Claimed distribution: (0.50, 0.20, 0.15, 0.15). Which hypotheses are appropriate for a chi-square goodness-of-fit test?

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