Practice Test 12 - AP Statistics

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

When performing a one-sample z-test for a population proportion, which condition justifies using a normal distribution to model the sampling distribution of the sample proportion?
A city compares mean response time (minutes) for two ambulance dispatch systems. Independent random samples of calls are taken from System 1 (S1) and System 2 (S2). A two-sample $t$ test for $\mu_{S1}-\mu_{S2}$ is performed with $H_0: \mu_{S1}-\mu_{S2}=0$ and $H_a: \mu_{S1}-\mu_{S2}>0$ . The p-value is 0.11. Using $\alpha=0.10$ , what conclusion is appropriate?
In a school cafeteria, let $X$ be the number of ounces of milk poured into a carton and $Y$ be the number of ounces spilled while carrying it. Assume $X$ and $Y$ are independent random variables with means $\mu_X=10$ and $\mu_Y=0.6$ , and standard deviations $\sigma_X=1.2$ and $\sigma_Y=0.5$ . Define a new random variable $N=X-Y$ , the number of ounces actually consumed. Which statement about $N$ is correct?
A candy company claims its assorted bag contains 5 colors in the following distribution: 20% red, 25% blue, 15% green, 30% yellow, and 10% orange. A student randomly selects 200 candies from a large shipment and records the observed counts shown in the table. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the company's claim? Observed counts table (n = 200): Red 36, Blue 54, Green 28, Yellow 62, Orange 20.
A candy company claims that in its "Tropical Mix" bag, the long-run distribution of candy colors is 30% yellow, 25% orange, 20% green, 15% pink, and 10% purple. A student randomly selects one bag and counts the colors with results shown in the table. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the company's claim? Observed counts table: Yellow 63, Orange 52, Green 41, Pink 29, Purple 15 Claimed distribution: (0.30, 0.25, 0.20, 0.15, 0.10).
A researcher compares the proportion of voters who support Candidate Z in two age groups. In random samples, 168 of 280 voters ages 18–34 support Z and 210 of 350 voters ages 35+ support Z. A 95% confidence interval for $p_{18\text{–}34} - p_{35+}$ is $( -0.03,\ 0.11)$ . The researcher claims that support is higher among voters ages 18–34 than among voters ages 35+. Is the claim supported by the confidence interval?
A public transit agency surveys a random sample of riders to estimate the proportion who would use a new late-night route. The agency will add the route if the estimate exceeds 40%, but adding it requires hiring drivers and buying fuel. If the estimate is too low, riders lose service; if too high, money is wasted. Why is it important to consider potential error when using the survey estimate to decide?
A university wants to know whether a new tutoring program improves calculus exam scores. Students choose whether to participate in tutoring. At the end of the term, the mean exam score of participants is 84, and the mean score of nonparticipants is 78. Which conclusion is supported by these data?
A city evaluated whether the proportion of commuters who use public transit differs between two years. In a random sample of 350 commuters surveyed in 2023, 98 reported using public transit; in a separate random sample of 360 commuters surveyed in 2025, 125 reported using public transit. A two-proportion $z$ test was conducted for $H_0: p_{2023}=p_{2025}$ versus $H_a: p_{2023}\ne p_{2025}$ , and the p-value was $0.009$ . Using $\alpha=0.05$ , what conclusion is appropriate?
A city randomly sampled 250 registered voters to estimate the proportion $p$ who support a proposed public transit tax. In the sample, 120 voters supported the tax. A 90% confidence interval for $p$ was reported as $(0.43, 0.53)$ . Which interpretation is correct?
A researcher compares mean reaction time for people who drank coffee (C) versus tea (T). A 95% confidence interval for the difference, $\mu_C-\mu_T$ , is $(-0.08,\ 0.01)$ seconds. The researcher claims: "Coffee leads to faster (smaller) mean reaction time than tea." Is the claim supported by the confidence interval?
A hospital reports that the mean waiting time in its emergency room is 42 minutes. A local news station believes the mean waiting time has changed and may not be 42 minutes anymore. They record waiting times for a random sample of 60 patients and find a sample mean of 45 minutes. Which hypotheses are appropriate for a one-sample test of a population mean waiting time?
A company compares delivery times from two warehouses. Many times, it takes an independent random sample of $n_1=25$ deliveries from Warehouse 1 and $n_2=64$ deliveries from Warehouse 2, then computes $\bar{x}_1-\bar{x}_2$ (in minutes). Which statement is correct about the sampling distribution of $\bar{x}_1-\bar{x}_2$ ?
A fitness coach compares mean resting heart rate (in beats per minute) for clients who follow a yoga program versus clients who follow a weight-training program. A random sample of 25 yoga clients had a mean resting heart rate of 62.7 bpm, and a random sample of 27 weight-training clients had a mean of 65.1 bpm. The coach's claim is that yoga leads to a lower mean resting heart rate than weight training. Which hypotheses are appropriate?
A city health department randomly sampled 400 adult residents and found that 236 reported getting a flu shot this season. A 95% confidence interval for the true proportion $p$ of all adult residents in the city who got a flu shot is $(0.54,\ 0.64)$ . Which interpretation is correct?
A nutrition researcher wants to test whether the mean sodium content of a certain brand of canned soup is less than the advertised value of 480 mg per serving. A random sample of $n=40$ cans is selected from recent production, and the sample mean sodium content is $\bar{x}=468$ mg. Which hypotheses are appropriate for a test of the population mean sodium content, $\mu$ ?
A company inspects items coming off an assembly line and keeps inspecting until the first defective item is found. A success is "defective," and the company records the number of defectives found. Does this meet binomial conditions for the number of successes?
A nutrition label on a snack bar says the mean sodium content is 140 mg per bar. A random sample of $n=30$ bars is tested, and the sample mean sodium content is $\bar{x}=145$ mg. A researcher wants to test the company's claim that the true mean sodium content is 140 mg (not higher or lower). Which hypotheses are appropriate for a test of a population mean?
Scores on a professional certification exam for all test takers are approximately Normal with mean $\mu=500$ and standard deviation $\sigma=80$ . A score of $x=660$ is marked. Which statement about the marked value is correct?
After collecting data on the number of years a person has been running and their time to complete a 10k race, a coach finds a negative linear association in her sample. Which question is most directly related to the statistical concept of inference for regression slope?

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