Practice Test 33 - AP Statistics

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

A city planner wants to know whether housing type is associated with whether residents support a new public transit proposal. From a single random sample of 300 residents, the planner records housing type (Apartment, Townhouse, Single-family) and support (Support, Oppose). The results are shown in the two-way table. Which chi-square test is appropriate, and what are the correct hypotheses? Note: One sample; two categorical variables.
A fitness study compares mean resting heart rate (bpm) for people who do yoga weekly vs people who do not. From two independent random samples, a 98% confidence interval for $(\mu_{yoga}-\mu_{no\ yoga})$ is $(-4.5, 0.8)$ . Which interpretation is correct?
A teacher claims the mean score on a standardized quiz for all students in a district is $\mu=75$ points. A random sample of students is selected and a 90% confidence interval for the population mean score is computed as $(74.1,\ 79.6)$ . Is the claim supported by the confidence interval?
A city council member claims that more than half of registered voters in the city support a proposed park. A random sample of 200 registered voters finds 118 who support it. A one-sample $z$ test for a population proportion is conducted with hypotheses $H_0: p=0.50$ and $H_a: p>0.50$ at significance level $\alpha=0.05$ . The test results in a $p$ -value of 0.041, so the null hypothesis is rejected. Which conclusion is appropriate?
A nutritionist sampled 20 adults and recorded daily sugar intake ( $x$ , grams) and fasting blood glucose ( $y$ ). A least-squares regression of $y$ on $x$ was fit and the slope test used $H_0: \beta_1=0$ vs. $H_a: \beta_1\ne 0$ . The p-value was 0.26 and the estimated slope was positive, so the nutritionist failed to reject $H_0$ at $\alpha=0.05$ . What conclusion is appropriate?
A school district wants to estimate the mean time (in minutes) it takes high school students to complete a certain standardized math assessment. A random sample of 30 students took the assessment, and a 98% confidence interval for the population mean completion time was found to be $(47.5,\ 52.9)$ minutes. Which interpretation is correct?
A website's page-load times for individual visits are highly right-skewed, with occasional extreme delays; the population is not normal. The site administrator repeatedly selects random samples of $n=60$ visits and computes the sample mean load time $\bar{x}$ . The sampling distribution of $\bar{x}$ is approximately normal. Why is the sampling distribution approximately normal?
A company compares two website designs to see which leads to a higher purchase rate. Of 200 randomly selected visitors shown Design 1, 34 made a purchase. Of 180 randomly selected visitors shown Design 2, 18 made a purchase. The company's research claim is that Design 1 has a higher purchase proportion than Design 2. Which hypotheses are appropriate for a test of the company's claim about the population proportions?
A hospital states that the mean wait time in its emergency department is $\mu=30$ minutes. A random sample of 35 patients is selected, and a one-sample $t$ test is performed with $H_0:\mu=30$ and $H_a:\mu>30$ at $\alpha=0.01$ . The p-value is 0.012. What conclusion is appropriate?
A school district wants to know if students at a particular high school sleep less than the recommended 8 hours per night on average. A random sample of 50 students reports their sleep, and the sample mean is $\bar{x}=7.45$ hours. Which hypotheses are appropriate for a test about the population mean sleep time $\mu$ ?
A company surveyed 250 employees about whether they work remotely at least 3 days per week and whether they report being satisfied with work-life balance. The results are shown. Which comparison is appropriate for assessing whether satisfaction is associated with remote-work status using conditional distributions? <table> <tr><th></th><th>Satisfied</th><th>Not satisfied</th></tr> <tr><td>Remote $\ge 3$ days</td><td>90</td><td>35</td></tr> <tr><td>Remote $<3$ days</td><td>72</td><td>53</td></tr> </table>
A sports analyst randomly sampled 300 fans attending games and found that 198 favor adding instant replay reviews. A 96% confidence interval for the true proportion $p$ of all fans who favor adding instant replay reviews is $(0.60,\ 0.72)$ . Which interpretation is correct?
A car magazine compared mean fuel efficiency (mpg) for cars using regular gasoline versus premium gasoline. From independent random samples, a 95% confidence interval for $(\mu_{\text{regular}}-\mu_{\text{premium}})$ was $( -2.7,\ 1.1)$ . Which interpretation is correct?
A city compares mean commute time (minutes) for residents who use public transit versus those who drive. From independent random samples, a 90% confidence interval for $(\mu_{\text{transit}}-\mu_{\text{drive}})$ is $(-3,\,12)$ . Which interpretation is correct?
A coach compared mean improvement (seconds) in a 100-meter sprint after two different training plans, using independent groups of athletes: Plan P and Plan Q. A 90% confidence interval for $\mu_P-\mu_Q$ is $(0.02,\ 0.15)$ seconds. Which interpretation is correct?
An environmental scientist models ozone level ( $y$ , in ppb) from traffic volume ( $x$ , in thousands of cars per day) using data from days with traffic between 10 and 60 (thousand cars). The regression line is $\hat{y}=18+1.1x$ . The purpose of the linear model is to describe the association and predict typical ozone levels for traffic volumes in the observed range. Which interpretation of the model is correct?
An environmental agency uses a sample of water tests from a river to estimate whether the mean pollutant level exceeds a legal limit. Declaring the river unsafe could trigger costly restrictions; failing to act when levels truly exceed the limit could harm public health. Why is it important to consider potential error in the inference before making a policy decision?
For a chi-square test of homogeneity, what would be the expected frequency of morning customers who prefer Espresso, assuming coffee preference is the same for both shifts?
A fitness app company asks: "Does enabling a daily step-goal notification increase average daily steps?" The population is all current app users. The proposed plan is to compare average steps for users who turn on notifications in the settings to users who do not, using one month of app data. Which aspect is most important to address before collecting data?
A cafeteria tracks two independent random variables: $X$ , the number of apples sold in a day with $\mu_X=120$ and $\sigma_X=15$ , and $Y$ , the number of bananas sold in a day with $\mu_Y=90$ and $\sigma_Y=12$ . Let $C=X-Y$ be the difference in sales (apples minus bananas). Which statement about $C$ is correct?

Practice tests