Practice Test 25 - AP Statistics

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

The weights of apples from an orchard have population mean $\mu=180$ grams. The distribution of individual apple weights is moderately skewed. A grocer repeatedly selects random samples of size $n=40$ apples and computes the sample mean weight $\bar{x}$ . Which statement about the sampling distribution of $\bar{x}$ is correct?
A beverage company is testing whether three advertising campaigns (A, B, C) lead to the same distribution of customer reactions (Positive, Neutral, Negative). The company runs each campaign in a different region and takes a separate random sample of customers exposed to that campaign, recording each customer's reaction. The results are in the two-way table. Which chi-square test is appropriate, and what are the correct hypotheses? Note: Multiple groups (campaigns) compared on one categorical response.
A student spins a fair spinner that can land on exactly one of four colors: {Red, Blue, Green, Yellow}. Let R be the event the spinner lands on Red. The student claims $P(R)=0.25$ . Which statement correctly describes the probability?
A streaming service wants to estimate the average number of hours per week its subscribers watch content. It takes a simple random sample of 500 subscribers from its current subscriber list and computes a sample mean of 9.4 hours per week. Which conclusion is supported by the data?
In a survey of 200 students, 90 reported that they play a sport (S), 120 reported that they have a part-time job (J), and 50 reported both playing a sport and having a part-time job. One student is selected at random. Let Event A be "the student plays a sport" and Event B be "the student has a part-time job." Which statement about Events A and B is correct?
A tech company is testing four versions of a phone app interface (V1–V4) to see which yields the shortest average task completion time. Users will test the app either on iOS or Android, and completion times differ by operating system. The company can recruit 200 users and randomly assign an interface version. Which experimental design is most appropriate?
A wildlife biologist believes that a certain species of bird uses four nesting areas (North, South, East, West) equally often. Over one breeding season, the biologist records the nesting area for each of 160 nests (one categorical variable with four categories). The question is whether the distribution differs from equal use. Which inference procedure is most appropriate?
A streaming service summarized the number of episodes watched in a single weekend by 100 users. The summaries were: mean $=9.6$ , median $=7$ , SD $=8.1$ , five-number summary $(0,\ 3,\ 7,\ 12,\ 45)$ , and IQR $=9$ . Which interpretation is correct?
A city engineer claims the mean time for a certain traffic light to complete one full cycle is $\mu=90$ seconds. A random sample of cycles is observed, producing a 99% confidence interval for the population mean cycle time: $(91.2\text{ s},\ 94.8\text{ s})$ . Is the claim supported by the confidence interval?
A grocery store tracked whether customers used a digital coupon and whether they purchased a store-brand product. The two categorical variables are Coupon use (Used/Did not use) and Store-brand purchase (Yes/No). Using the two-way table, which comparison is appropriate for assessing whether coupon use is associated with purchasing store-brand? Which comparison is appropriate?
A teacher randomly selects a student and notes whether the student completed the homework (event $A$ ) and whether the student attended after-school tutoring that week (event $B$ ). The teacher suspects tutoring attendance is associated with homework completion. How does knowing that $B$ occurred affect the likelihood of $A$ ?
Which of the following statements best describes the relationship between a frequency and a relative frequency for a given category?
A school principal claims that at least 80% of students eat breakfast on school days. A random sample of students is taken, and the 90% confidence interval for the population proportion who eat breakfast is $(0.77, 0.83)$ . Is the claim supported by the confidence interval?
A tech blog estimates the proportion $p$ of its readers who prefer dark mode. From a random sample of 1,200 readers, a 97% confidence interval for $p$ is $(0.58, 0.64)$ . Which interpretation is correct?
A medical researcher wants to compare the effect of three doses of a supplement (0 mg, 50 mg, 100 mg) on reaction time. Reaction time is also affected by time of day (morning, afternoon, evening). The researcher can run 9 sessions total and can recruit one participant per session (different participant each session). The researcher wants each dose tested once at each time of day to control for time-of-day effects without increasing the number of sessions. Which experimental design is most appropriate?
A health researcher compares the proportion of adults who get at least 7 hours of sleep on weeknights in two regions. In random samples, Region A had 312 of 500 adults meeting the guideline and Region B had 290 of 520 meeting the guideline. A 95% confidence interval for $p_A - p_B$ is $(-0.01,\ 0.14)$ . The researcher claims that Region A has a higher sleep-guideline rate than Region B. Is the claim supported by the confidence interval?
A school compares the proportion of students who prefer online homework in Grade 9 versus Grade 10. A 95% confidence interval for the difference in proportions, defined as $p_9 - p_{10}$ , is $(0.03,\ 0.17)$ . A student claims, "Grade 9 has a higher proportion of students who prefer online homework than Grade 10." Is the claim supported by the confidence interval?
An environmental agency tests whether the mean level of a pollutant in a river exceeds the legal limit of 10 ppm. They test $H_0: \mu=10$ vs. $H_a: \mu>10$ at $\alpha=0.01$ . The p-value is 0.008, so they reject $H_0$ and conclude the mean pollutant level exceeds 10 ppm. In reality, the true mean pollutant level is $\mu=12$ ppm. Which type of error was made?
An environmental scientist recorded data from 25 lakes on water temperature ( $x$ , in $^\circ$ C) and dissolved oxygen ( $y$ , mg/L). A least-squares regression of $y$ on $x$ was fit. A test of the slope used $H_0: \beta_1=0$ vs. $H_a: \beta_1\ne 0$ and produced a p-value of 0.41, with an estimated negative slope. Using $\alpha=0.05$ , the scientist failed to reject $H_0$ . What conclusion is appropriate?
What is the expected number of weekdays with Low customer traffic if traffic level is independent of the type of day?

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