Practice Test 91 - AP Statistics

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

A game booth advertises that players win a small prize 30% of the time. A group of friends plays independently 15 times and wins 9 prizes (60%). They expected around 4 or 5 wins, but observed 9. Is the result unexpected, given the variability in the number of wins for only 15 plays if the true win probability is 30%?
A city tests whether a new traffic signal timing reduces the mean commute time. They test $H_0: \mu=32$ minutes vs. $H_a: \mu<32$ at $\alpha=0.05$ . The p-value is 0.01, so they reject $H_0$ and conclude mean commute time is reduced. In reality, the true mean commute time with the new timing is $\mu=30$ minutes. Which type of error was made?
A nutritionist compares mean LDL cholesterol for adults following Diet X versus Diet Y after 8 weeks. A 95% confidence interval for $\mu_X-\mu_Y$ is reported as $(-18,\ -4)$ mg/dL. The nutritionist claims: "Diet X results in a lower mean LDL cholesterol than Diet Y." Is the claim supported by the confidence interval?
In a city survey, residents are classified by whether they commute by public transit (event $A$ ) and whether they live within 1 mile of a subway station (event $B$ ). Because distance to a station may influence commuting choices, the events may not be independent. How does knowing that $B$ occurred affect the likelihood of $A$ ?
A researcher compares the proportion of plants that survive under two fertilizers. Fertilizer A is tested on a random sample of $n_1=100$ plants and Fertilizer B on an independent random sample of $n_2=25$ plants; $\hat p_1$ and $\hat p_2$ are the sample survival proportions. Consider the sampling distribution of $\hat p_1-\hat p_2$ over repeated experiments. Which statement is correct?
A university reports that SAT Math scores for its applicants are approximately Normal with mean $\mu=600$ and standard deviation $\sigma=80$ for the population of applicants this year. A particular applicant has a score of 760. Which statement about the marked value is correct?
A researcher records, for 12 runners, weekly training time (hours per week) and 5K race time (minutes). The scatterplot shows a clear downward linear trend with moderate strength and one possible high-leverage point at very high training time. Which statement about correlation is correct?
A school surveyed 200 students about whether they participated in a school sport this year and whether they reported sleeping at least 8 hours on most school nights. The two-way table shows the results. Which comparison is appropriate for assessing whether sleep amount is associated with sports participation using conditional distributions? <table> <tr><th></th><th> $\ge 8$ hours</th><th> $<8$ hours</th></tr> <tr><td>Plays a sport</td><td>54</td><td>46</td></tr> <tr><td>Does not play a sport</td><td>38</td><td>62</td></tr> </table>
A state agency randomly sampled 1,000 drivers to estimate the proportion $p$ who support a new hands-free law. In the sample, 610 drivers supported the law. A 95% confidence interval for $p$ was reported as $(0.58, 0.64)$ . Which interpretation is correct?
A researcher tests whether a new tutoring program increases the mean math score above 75. For a random sample of students in the program, a one-sample $t$ test is run for $H_0: \mu = 75$ versus $H_a: \mu > 75$ at $\alpha = 0.05$ , resulting in p-value $p = 0.049$ . Which interpretation of the p-value is correct?
A weather app records tomorrow's forecast for a city. Define event $A$ as "tomorrow's forecast includes rain" and event $B$ as "tomorrow's forecast includes thunderstorms." The app allows multiple conditions to be listed for the same day. Are the two events mutually exclusive?
A university wants to estimate the proportion of all undergraduate students who support a proposed change to the dining plan. The university emails the survey link to every undergraduate, and 1,450 students choose to respond. Which statement best describes the sample representativeness?
A website claims that 50% of visitors click a certain button. A student believes the true click rate is about 50% and records the next 200 visitors; 120 clicked the button (60%). The student asks whether this outcome is surprising just due to random sampling variability with $n=200$ if the true rate really is 50%. Is the result unexpected?
A streaming service compares the proportion of users who watch documentaries among subscribers in Region East versus Region West. A 95% confidence interval for $p_E - p_W$ is $(0.08, 0.11)$ . An analyst claims, "A higher proportion of subscribers in the East watch documentaries than in the West." Is the claim supported by the confidence interval?
A local news station asks: "What proportion of city residents support building a new sports arena?" The population is all adult residents of the city. The proposed plan is to stand outside the arena at a weekend event and interview as many adults as possible about whether they support the new arena. Which aspect is most important to address before collecting data?
For $H_0:p=0.5$ , $\hat p=0.6$ , $n=100$ , which is the z-test statistic?
A dermatologist is studying whether two different acne creams reduce the number of inflamed spots after 6 weeks. One hundred patients are recruited from a clinic. Patients are randomly assigned to one of three treatments: Cream A, Cream B, or a placebo cream with no active ingredient. The response variable is the number of inflamed spots after 6 weeks. Which design element best helps isolate the effect of the active ingredients from other factors?
A university compared the proportion of students who report high stress in two independent random samples: 64 of 180 first-year students and 70 of 200 seniors reported high stress. A two-proportion $z$ test at $\alpha=0.05$ tested $H_0: p_F=p_S$ versus $H_a: p_F\ne p_S$ , where $p_F$ and $p_S$ are the true high-stress proportions for first-years and seniors. The p-value was 0.62. What conclusion is appropriate?
An airline tests whether the mean arrival delay is less than 10 minutes. They test $H_0: \mu=10$ versus $H_a: \mu<10$ at $\alpha=0.05$ . They fail to reject $H_0$ and do not advertise improved on-time performance. In truth, the mean arrival delay is $\mu=7$ minutes. Which type of error was made?
A school district wants a point estimate of the population proportion $p$ of all high school students in the district who get at least 8 hours of sleep on a typical school night. The district selects a simple random sample of 200 students from the full enrollment list and computes the sample proportion $\hat p$ who report at least 8 hours. The district reports $\hat p$ as the point estimate for $p$ . Which statement describes whether the estimate is biased?

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