Practice Test 78 - 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 website claims that 50% of visitors click a certain button. A student expects about 50 clicks in a random sample of 100 visitors. In one sample of 100 visitors, only 41 click the button. Is this result unexpected, given the typical variability in sample proportions for $n=100$ ?
A public health analyst uses least-squares regression to predict systolic blood pressure ( $y$ , mmHg) from sodium intake ( $x$ , mg/day) using a random sample of 35 adults. A 95% confidence interval for the population slope is $(0.001, 0.006)$ mmHg per mg/day. Which interpretation is correct?
A nonprofit compares the proportion of donors who give again the next year between two fundraising approaches. Independent random samples were taken, and a 96% confidence interval for the difference in repeat-donation proportions (Approach New minus Approach Traditional) is $(0.01, 0.09)$ . Which interpretation is correct?
A university dining hall tracks the number of cookies students take at lunch. The population distribution is heavily right-skewed because most students take 0–2 cookies, but a few take many. The manager repeatedly selects random samples of $n=80$ students and computes the sample mean number of cookies $\bar{x}$ . He considers the sampling distribution of $\bar{x}$ . Why is the sampling distribution approximately normal?
A meteorologist records, over 18 days, humidity (percent) and high temperature (°F). The scatterplot shows a fairly strong downward linear association. Which statement about correlation is correct?
A commuter takes the train for 22 weekdays and records whether the train is late each day. A success is "late," and exactly 22 days are observed. The probability of lateness is higher on days with heavy rain, and several of the 22 days are rainy. Does this meet binomial conditions?
A researcher tests whether listening to a guided meditation audio reduces stress. The explanatory variable is audio type (guided meditation vs. neutral audiobook), and the response variable is a stress score from a questionnaire after 2 weeks. Participants are randomly assigned to one of the two audios, and both audios are delivered through identical-looking apps labeled only "Audio 1" and "Audio 2," so participants do not know which type they receive. Which feature is primarily intended to reduce the placebo effect?
A phone's battery percentage decreases during two independent time periods. Let $D_1$ be the percent drop during the morning and $D_2$ be the percent drop during the afternoon. Assume $\mu_{D_1}=22$ , $\sigma_{D_1}=6$ , $\mu_{D_2}=28$ , and $\sigma_{D_2}=5$ . Let $D=D_1+D_2$ be the total percent drop. Which statement about $D$ is correct?
A streaming service claims that the proportion of its users who prefer each of five genres is: 40% drama, 25% comedy, 15% action, 10% documentary, and 10% sci-fi. A random sample of 300 users is surveyed, producing the observed counts below. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the company's claim?
A smartphone company claims that only 8% of its phones are returned within 30 days. A consumer group randomly sampled 150 purchases and found 20 returns. A one-proportion $z$ test was performed for $H_0: p=0.08$ versus $H_a: p>0.08$ at $\alpha=0.01$ . The test resulted in a $p$ -value of 0.034, so the group failed to reject $H_0$ . Which conclusion is appropriate?
A manufacturer states that defects in its products fall into 5 categories with proportions 0.50, 0.20, 0.15, 0.10, and 0.05. An auditor reviews 100 defects and records the counts shown in the table. A chi-square goodness-of-fit test is performed for $H_0$ : the defect-category distribution matches the stated proportions vs. $H_a$ : it does not. The p-value is 0.0006. What conclusion is appropriate at the $\alpha=0.01$ level? Observed/Expected counts and p-value: - p-value = 0.0006
A wildlife center recorded whether rescued birds were treated with a new rehabilitation protocol (New/Standard) and whether they were successfully released (Released/Not Released). The table summarizes outcomes. Which comparison is appropriate for assessing whether release success is associated with protocol type? Categorical variables: Protocol type and Release outcome.
A machine produces bolts with mean length $\mu=5.0$ cm. A quality engineer repeatedly selects random samples of $n=100$ bolts and computes the sample mean length $\bar{x}$ . Assume the sampling distribution of $\bar{x}$ is approximately normal. Which statement about the sampling distribution is correct?
A coach wants to estimate the mean resting heart rate of athletes in a large training program. Two independent random samples of 30 athletes each were selected from the same roster. Sample 1 had a mean resting heart rate of 62 bpm; Sample 2 had a mean of 66 bpm. Measurements were taken using the same device and protocol. Why might the sample results differ?
A health clinic claims that at most 30% of its patients miss at least one scheduled appointment each year. A random sample is taken and a 95% confidence interval for the population proportion who miss at least one appointment is $(0.27, 0.33)$ . Is the claim supported by the confidence interval?
A researcher measured the reaction time (in milliseconds) for 100 adults on a computer task. The summaries were: mean = 280 ms, median = 265 ms, SD = 55 ms, five-number summary = (min 190, $Q_1$ 240, median 265, $Q_3$ 300, max 520), and IQR = 60 ms. Which interpretation is correct?
A streaming service randomly sampled 500 subscribers to estimate the proportion $p$ who watched a particular new series in its first week. In the sample, 165 subscribers watched it. A 96% confidence interval for $p$ was computed as $(0.30, 0.36)$ . Which interpretation is correct?
A public health department tests whether the proportion of residents who support a proposed policy is greater than 0.50. They test $H_0: p=0.50$ vs. $H_a: p>0.50$ at $\alpha=0.05$ . The p-value is 0.11, so they fail to reject $H_0$ and conclude there is not convincing evidence that more than half support the policy. In reality, the true proportion is $p=0.58$ . Which type of error was made?
Two brands of batteries are tested for mean lifetime (hours). Brand A had a sample mean lifetime of 9.8 hours and Brand B had 10.1 hours. A 95% confidence interval for the difference in population means, defined as $\mu_A-\mu_B$ , is $(-0.9, -0.1)$ . A consumer claims, "Brand B lasts longer on average than Brand A." Is the claim supported by the confidence interval?

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