Practice Test 90 - AP Statistics

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

A political scientist compares support for a ballot measure between two age groups. In a random sample of 140 voters ages 18–34, 79 support the measure. In a random sample of 160 voters ages 35+, 78 support the measure. The research claim is that the proportion supporting the measure is higher among ages 18–34. Which hypotheses are appropriate for testing this claim using two population proportions?
A teacher records the scores (out of 100) on a quiz for 80 students. The five-number summary is: minimum $40$ , $Q_1=62$ , median $70$ , $Q_3=84$ , maximum $98$ . A boxplot is made using these values. Which feature is consistent with the summary statistics?
A card is drawn at random from a standard 52-card deck. The sample space is all 52 distinct cards, and the event of interest is drawing a heart. The probability is $P(\text{Heart})=\frac{13}{52}=0.25$ . Which statement correctly describes the probability $0.25$ ?
A manager recorded the time (in minutes) it took each employee in a department to complete a required safety quiz (population: all 50 employees in the department). The five-number summary is: min $=6$ , $Q_1=9$ , median $=12$ , $Q_3=15$ , max $=28$ . A boxplot is drawn. Which feature is consistent with the summary statistics?
A researcher investigates the relationship between hours of weekly exercise and resting heart rate for adults at a large company. They take a random sample of 30 adults and calculate the slope of the least-squares regression line. If they were to take a second, independent random sample of 30 adults from the same company, which of the following is most likely to be true?
A store tracks two independent random variables: $X$ , the amount (in dollars) a customer spends on groceries, with $\mu_X=42$ and $\sigma_X=8$ , and $Y$ , the amount (in dollars) the same customer spends on household items, with $\mu_Y=18$ and $\sigma_Y=5$ . Define $D=X-Y$ (difference in spending). Which statement about $D$ is correct?
A school counselor claims that the long-run distribution of students' preferred study times is 25% morning, 45% afternoon, and 30% evening. A random sample of 120 students is surveyed with results shown. Observed counts table: Morning 22, Afternoon 61, Evening 37 Claimed distribution: (0.25, 0.45, 0.30). Which hypotheses are appropriate for a chi-square goodness-of-fit test?
An observation of this trend is the first step in investigating a relationship between which two variables?
A tech company compares the proportion of users who enable two-factor authentication (2FA) on two app versions. In independent random samples, 410 of 800 users on Version 1 enabled 2FA and 372 of 820 users on Version 2 enabled 2FA. A 95% confidence interval for $p_1 - p_2$ is $(0.01,\ 0.11)$ . Which interpretation is correct?
A nutritionist claims the mean sodium content of a brand's "low-sodium" soup is $\mu=480$ mg per serving. A random sample of servings is used to construct a 95% confidence interval for the population mean sodium content: $(462\text{ mg},\ 498\text{ mg})$ . Is the claim supported by the confidence interval?
A fitness app claims that the mean number of steps its users take per day is 8,000. A researcher suspects the true mean for all users is lower. A random sample of $n=60$ users shows a mean of $ overline{x}=7,650$ steps. Which hypotheses are appropriate for testing the researcher's claim about the population mean steps, $\mu$ ?
A school wants to estimate the proportion of students who usually eat breakfast on school days. Two different students each take an independent simple random sample of 60 students from the same school on the same week. Sample 1 finds 34 of 60 say they usually eat breakfast, while Sample 2 finds 27 of 60 say they usually eat breakfast. Both students followed the same sampling method, and the question wording was identical. Why might the sample results differ?
A wildlife agency investigates the research question: "What is the mean weight of adult trout in Lake Orion?" Biologists used nets at two easily accessible shoreline locations on a single afternoon and weighed 60 adult trout; the sample mean weight was 1.8 kg. They concluded that the mean weight of adult trout in Lake Orion is about 1.8 kg. Which statement explains whether the conclusion is valid?
A county health department wants to estimate the proportion of all adults in the county who received a flu shot this year. The county is divided into 10 towns. The department randomly selects 2 towns and then surveys every adult who visits the main pharmacy in each selected town during one Saturday. Which statement best describes the sample representativeness?
A psychologist compares mean reaction time (milliseconds) for participants after listening to music versus sitting in silence. Independent random samples were taken, and a 90% confidence interval for $(\mu_{\text{music}}-\mu_{\text{silence}})$ is $(-25,\,-5)$ . Which interpretation is correct?
A political analyst randomly samples 1,000 likely voters to estimate the proportion who approve of the current governor. The analyst wants to claim that the approval rate is 52% (that is, $p=0.52$ ). A 95% confidence interval for the population proportion approving is $(0.49, 0.55)$ . Is the claim supported by the confidence interval?
A streaming service randomly sampled 500 subscribers to estimate the proportion $p$ of all subscribers who prefer watching on a TV rather than a phone or tablet. In the sample, 295 preferred TV. A 95% confidence interval for $p$ is $(0.55,\ 0.63)$ . Which interpretation is correct?
A streaming company tests whether a new recommendation algorithm increases the mean number of minutes watched per user above the current mean of 50 minutes. They test $H_0: \mu=50$ versus $H_a: \mu>50$ at $\alpha=0.05$ . The result is statistically significant, so they conclude the algorithm increases watch time. In reality, the true population mean with the new algorithm is $\mu=50$ minutes (no change). Which type of error was made?
For a large population of car trips, the mean fuel economy is $\mu=27$ mpg with population standard deviation $\sigma=5$ mpg. The distribution of individual mpg values is bimodal because it mixes city and highway driving. A researcher repeatedly takes random samples of size $n=45$ trips and computes the sample mean mpg $\bar{x}$ . Which statement about the sampling distribution of $\bar{x}$ is correct?
A teacher recorded scores (out of 100) on a quiz for 40 students. The summaries were: mean = 78.6, median = 82, SD = 10.2, five-number summary = (min 45, $Q_1$ 74, median 82, $Q_3$ 88, max 94), and IQR = 14. Which interpretation is correct?

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