Practice Test 28 - AP Statistics

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

A city transportation department claims that riders' primary mode of commuting is distributed as Car 55%, Bus 20%, Train 15%, Bike/Walk 10%. A random sample of $n=250$ commuters is surveyed, and the observed counts are shown in a table. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the department's claim?
A parking garage records the number of minutes a randomly selected car spends searching for a space (rounded to the nearest minute). Let $X$ be this search time, a discrete random variable with mean $\mu_X=5.0$ minutes and standard deviation $\sigma_X=3.2$ minutes. Which interpretation of the mean is correct?
A quality-control engineer states that the probability a randomly selected light bulb from a factory's output is defective is $0.02$ . The random process is selecting one bulb at random; the sample space is {defective, not defective}. Which statement correctly describes the probability $0.02$ ?
A researcher wishes to test whether the majority of adults in a large city prefer coffee over tea. A random sample of 300 adults from the city will be surveyed. What is the parameter of interest for this significance test?
A school counselor believes that 40% of students prefer online appointments. To estimate the probability that in a random sample of 12 students, at least 7 prefer online appointments, a student runs a simulation: for each trial, generate 12 random digits where 0–3 represent "online" and 4–9 represent "not online," then count whether the trial has 7 or more online. After 1000 trials, 271 trials met the condition. Which interpretation of the simulation results is correct?
A researcher wants to study whether a new study-skills workshop improves test scores for students in an introductory college course. The plan is to invite all students to attend the workshop, then compare the average exam score of those who choose to attend with those who do not. The research question is: "Does attending the workshop cause higher exam scores for students in this course?" Which aspect is most important to address before collecting data?
A boxplot has Q1=40, median=50, Q3=80. Which description is most plausible?
A spinner is divided into 8 equal sectors labeled 1 through 8. The spinner is spun once. Let Event A be "the result is a multiple of 2" and Event B be "the result is a multiple of 4." Which statement about Events A and B is correct?
A quality-control engineer inspects a shipment by randomly selecting 25 lightbulbs and checking whether each one is defective. Historical data suggest that any inspected bulb has a 0.04 probability of being defective, and each inspection is treated as independent. If $X$ is the number of defective bulbs found, which values correctly model this situation with a binomial distribution (identify $n$ and $p$ )?
A coach wants to compare two training programs (P1 vs. P2) on athletes' sprint times. Sprint times differ by position group (sprinters vs. middle-distance), and the coach can assign athletes within each position group to a program. However, the coach wants each athlete to follow only one program for the season. Which experimental design is most appropriate to control for position group while comparing programs?
A scientist compares average concentration levels in two independent chemical processes. In each repetition, she takes an independent random sample of $n_1=36$ measurements from Process 1 and $n_2=49$ measurements from Process 2 and calculates $\bar{x}_1-\bar{x}_2$ . The processes have means $\mu_1,\mu_2$ and standard deviations $\sigma_1,\sigma_2$ . Which statement is correct about the center of the sampling distribution of $\bar{x}_1-\bar{x}_2$ ?
The lifetimes of a certain brand of light bulb (population of all bulbs of this brand) are approximately Normal with mean $\mu=1200$ hours and standard deviation $\sigma=150$ hours. A normal curve is shown with the value $1050$ hours marked. Normal curve (hours) | | .-''''-. | .-' '-. | .' '. | / \ |----------|----|----|----|----|----|----|----> x 750 900 1050 1200 1350 1500 1650 1050 \mu=1200 Which statement about the marked value is correct?
A nutrition label claims that 40% of customers prefer a new granola bar flavor. A company surveys a random sample of 120 customers and finds 54 who prefer the new flavor. They run a one-sample $z$ test for a population proportion with $H_0: p=0.40$ versus $H_a: p\ne 0.40$ at $\alpha=0.05$ . The $p$ -value is 0.27, so they do not reject $H_0$ . Which conclusion is appropriate?
A teacher believes that the mean score on a certain standardized math test for students in the district is 500. A principal suspects the district's true mean score is higher than 500. A random sample of 80 students takes the test, and the sample mean score is 512. Which hypotheses are appropriate for a one-sample test of a population mean score?
SAT Math scores for the population of seniors at a large high school are approximately Normal with mean $\mu=560$ and standard deviation $\sigma=80$ . A normal curve is shown with the value $640$ marked. Normal curve (SAT Math) | | .-''''-. | .-' '-. | .' '. | / \ |----------|----|----|----|----|----|----|----> x 320 400 480 560 640 720 800 \mu=560 640 Which statement about the marked value is correct?
A gym claims that the mean weight loss for members after 8 weeks on a program is $\mu=6$ pounds. A random sample of 16 members is selected, and a one-sample $t$ test is conducted: $H_0:\mu=6$ vs. $H_a:\mu>6$ , using $\alpha=0.05$ . The p-value is 0.27. What conclusion is appropriate?
A warehouse has a very large inventory, and 18% of items are labeled fragile. A worker repeatedly takes many random samples of $n=90$ items (without replacement) and computes $\hat p$ . Which statement about the sampling distribution is correct?
A nutritionist measured the sodium content (in mg) of 40 frozen meals sold at a grocery store. The summaries were: mean $=720$ , median $=710$ , SD $=95$ , five-number summary $(520,\ 650,\ 710,\ 780,\ 900)$ , and IQR $=130$ . Which interpretation is correct?
An environmental group claims that at least 40% of households in a region recycle regularly. A random sample of 350 households found 126 that recycle regularly. A one-sample $z$ test for a population proportion was conducted at $\alpha=0.05$ with $H_0: p=0.40$ versus $H_a: p<0.40$ . The $p$ -value was 0.009, so the analyst rejected $H_0$ . Which conclusion is appropriate?
An educator compares mean quiz scores (out of 20 points) for students taught with a new interactive method versus a traditional lecture method. A random sample of $n=26$ interactive-method students had a mean score of $\bar{x}=16.8$ , and a random sample of $n=24$ lecture-method students had a mean score of $\bar{x}=15.9$ . The educator's claim is that the interactive method changes the population mean quiz score (could be higher or lower). Which hypotheses are appropriate?

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