Practice Test 84 - AP Statistics

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

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1. A manager models weekly sales (in thousands of dollars) from the number of online ads purchased. The manager claims that buying more ads has no linear effect on weekly sales. A 95% confidence interval for the slope is $(-0.8, 1.1)$ thousand dollars per ad. Is the claim supported by the confidence interval?
2. A museum records the amounts (in dollars) donated by 60 visitors during a weekend fundraiser. The five-number summary is: min $=1$, $Q_1=5$, median $=12$, $Q_3=25$, max $=120$. A modified boxplot (1.5·IQR rule) is drawn. Which feature is consistent with the summary statistics?
3. A warehouse records weights. Let $X$ be the weight (in pounds) of a randomly selected small box and $Y$ be the weight (in pounds) of a randomly selected large box. Assume $X$ and $Y$ are independent, with $\mu_X=18$, $\sigma_X=2$, $\mu_Y=32$, and $\sigma_Y=3$. Define $W=X+Y$, the total weight when shipping one small and one large box together. Which statement about $W$ is correct?
4. A botanist claims that plants grown under blue light have a greater mean height after 6 weeks than plants grown under white light. A 95% confidence interval for $(\mu_{\text{blue}}-\mu_{\text{white}})$ is $(-1.4,\ -0.2)$ cm. Is the claim supported by this interval?
5. A company tracks the number of defects on individual circuit boards. The population mean is $\mu=1.6$ defects per board with population standard deviation $\sigma=1.2$. Each day, an inspector randomly selects $n=49$ boards and computes the sample mean number of defects $\bar{x}$. This is repeated many times. Which statement about the sampling distribution of $\bar{x}$ is correct?
6. A city planner investigates whether neighborhood type is associated with monthly water use. For each of 45 households (observational units), the planner records neighborhood type coded as 1 = urban, 2 = suburban, 3 = rural, and monthly water use in gallons. The goal is to use neighborhood type to help explain differences in water use. Which classification is correct?
7. A grocery store wants to estimate the mean amount (in dollars) customers spend per visit. Two independent SRSs of 50 receipts from the same week are selected from all receipts that week. Sample 1 has a mean of $32.40, while Sample 2 has a mean of $29.10. Both samples were selected randomly from the same set of receipts. Why might the sample results differ?
8. A company advertises that only 8% of its light bulbs are defective. A quality-control inspector tests this claim by randomly selecting 150 bulbs and finding 20 defective. A one-sample proportion test is conducted at $\alpha=0.01$ with $H_0:p=0.08$ and $H_a:p>0.08$. The test produces a $p$-value of 0.0006, so the decision is to reject $H_0$. Which conclusion is appropriate?
9. A phone's face-recognition system attempts to unlock the device. The outcome is either "Success" or "Failure." The manufacturer reports $P(\text{success})=0.95$ under typical conditions. Let event $S$ be "the next attempt is successful." Which statement correctly describes the probability $P(S)=0.95$?
10. A nutritionist examines the relationship between daily fiber intake ($x$, in grams) and LDL cholesterol level ($y$, in mg/dL) for 60 adults. A 95% confidence interval for the true slope is $(-2.4,\ -0.6)$ mg/dL per gram. Which interpretation is correct?
11. A pharmacist investigates whether dosage of a medication in mg ($x$) predicts reduction in systolic blood pressure in mmHg ($y$) after one week. The pharmacist claims that higher dosage leads to greater reduction (larger $y$) in the population. Which hypotheses are appropriate for testing this claim about the population regression slope?
12. A fitness coach compares the mean number of push-ups completed in 1 minute for clients using two training plans. A random sample of 30 clients using Plan A had a mean of 41.3 push-ups, and a random sample of 29 clients using Plan B had a mean of 39.7 push-ups. The coach's research claim is that Plan A increases the mean number of push-ups compared with Plan B. Which hypotheses are appropriate for a two-sample $t$ test comparing population means?
13. A gardener compares mean plant height after 8 weeks for plants given Fertilizer 1 versus Fertilizer 2. Two independent random samples were used (Fertilizer 1: $n=20$; Fertilizer 2: $n=20$). A two-sample $t$ test for $\mu_1-\mu_2$ was performed with $H_0:\mu_1-\mu_2=0$ and $H_a:\mu_1-\mu_2\neq 0$. The p-value was 0.032. Using $\alpha=0.05$, what conclusion is appropriate?
14. At a small clinic, $X$ is the number of patients who arrive during a randomly selected 30-minute interval. The distribution of $X$ has mean $\mu_X=6.7$ and standard deviation $\sigma_X=2.9$. Which interpretation of the mean is correct?
15. A public health study compares the proportion of adults who received a flu shot in two counties. In County X, 156 of 260 adults in a random sample received a flu shot; in County Y, 170 of 300 adults in a random sample received a flu shot. A 95% confidence interval for $(p_X - p_Y)$ is $(-0.06, 0.12)$. Which interpretation is correct?
16. A hospital administrator believes that a new triage protocol reduces the mean waiting time in the emergency department to less than 45 minutes. After implementing the protocol, a random sample of 30 patients has a mean waiting time of $\bar{x}=41.8$ minutes. Which hypotheses are appropriate for testing the administrator's belief about the population mean waiting time $\mu$?
17. A bakery randomly selects one cookie from today's batch and records whether it is Chocolate chip (C), Oatmeal (O), or Sugar (S), so the sample space is $\{C, O, S\}$. The baker estimates $P(O)=0.30$ for today's batch. Which statement correctly describes the probability $0.30$ in this context?
18. A school district wants to estimate the proportion of all high school students in the district who get at least 8 hours of sleep on school nights. The population is all students in grades 9–12 across the district's 4 high schools. A researcher visits the district's website, lists every student ID, and uses a random number generator to select 250 IDs; those students are emailed a survey. After two reminders, 138 students respond. Which statement best describes the sample representativeness?
19. A restaurant chain wants to estimate the proportion of all customers nationwide who would recommend the chain to a friend. The chain randomly selects 60 of its 600 locations, then at each selected location surveys the first 10 customers who enter on a Monday morning. Which statement best describes the sample representativeness?
20. A university suspects that more than 25% of its students have taken at least one online course. A random sample of 120 students found 40 who had taken at least one online course. A one-sample $z$ test for a population proportion was conducted at $\alpha=0.05$ with $H_0: p=0.25$ and $H_a: p>0.25$. The $p$-value was 0.004, so the university rejected $H_0$. Which conclusion is appropriate?

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