Practice Test 93 - AP Statistics

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

A state election office claims that the proportion of registered voters who support a proposed ballot measure is less than $50\%$ . A polling organization takes a random sample of $n=500$ registered voters and finds $270$ support the measure (so $\hat{p}=0.54$ ). Which hypotheses are appropriate for testing the state office's claim?
A survey suggests that 19% of adults have run a marathon. Many random samples of $n=500$ adults are taken and $\hat p$ is computed each time. Which statement about the sampling distribution is correct?
In a town, 40% of households have a dog, 30% have a cat, and 10% have both a dog and a cat. A household is selected at random. Let Event $A$ be "has a dog," and Event $B$ be "has a cat." Which statement about Events $A$ and $B$ is correct?
To compare two fertilizers, an agronomist measured the mean height of plants after 6 weeks for independent plots using Fertilizer X and Fertilizer Y. A 95% confidence interval for $\mu_X-\mu_Y$ is $( -1.5,\ 0.9)$ cm. Which interpretation is correct?
A gym randomly samples 70 members and estimates the mean number of visits per month. A 90% confidence interval for the population mean is $(6.8, 8.1)$ visits. A manager claims the true mean number of visits is 6.5 per month. Is the claim supported by the confidence interval?
A bag contains only chocolate, vanilla, and strawberry candies. One candy is selected at random. Define event $A$ as "the candy is chocolate" and event $B$ as "the candy is not chocolate." The candy selected must be exactly one flavor. Are the two events mutually exclusive?
A city's water department states that the mean lead concentration in tap water is 5 parts per billion (ppb). A public health researcher wants to check whether the true mean lead concentration is different from 5 ppb. A random sample of 50 homes is tested, and the sample mean lead concentration is 5.8 ppb. Which hypotheses are appropriate for a one-sample test of a population mean lead concentration?
A researcher compares average commute distance (miles) for two independent groups: people who work remotely 1 day/week (R) and people who work remotely 0 days/week (N). In repeated sampling, she takes an SRS of $n_R=30$ and an SRS of $n_N=30$ and computes $\bar{x}_R-\bar{x}_N$ . Which statement is correct about the shape of the sampling distribution of $\bar{x}_R-\bar{x}_N$ ?
A basketball player makes 75% of her free throws in practice. In a game she shoots 8 free throws and makes only 2. The coach expected about 6 makes, but observed 2. Assuming the 75% rate is accurate and shots are independent, is the result unexpected due to random variability?
A delivery service records the number of packages delivered per driver per day. The population distribution is discrete and not normal, with a long right tail during peak seasons. A random sample of $n=40$ driver-days is selected, and the sample mean number of packages is computed. Why is the sampling distribution of $\bar{x}$ approximately normal?
A school compared two ways to invite students to a tutoring session (Email vs Text) and recorded whether each student attended. The purpose is to compare the conditional proportions of attending between invitation methods. Based on the two-way table, which comparison is supported by the data? Two-way table of Invitation Method by Attendance (proportions of all students): - Email & Attended: 0.18, Email & Did not attend: 0.32 - Text & Attended: 0.22, Text & Did not attend: 0.28
A teacher shuffles a standard 52-card deck and deals the top 20 cards face up. In those 20 cards, 15 are red and 5 are black. Under random shuffling, you expect some variation from a 50/50 split, and occasionally the split can be quite uneven. Is the pattern consistent with random behavior?
A political scientist tests whether the proportion of voters who approve of a policy is less than 0.40. The hypotheses are $H_0: p=0.40$ versus $H_a: p<0.40$ , with $\alpha=0.05$ . The p-value is 0.20. Which interpretation of the p-value is correct?
An ecologist measured 10 ponds for water temperature ( $x$ , in °C, from 12 to 24) and dissolved oxygen ( $y$ , in mg/L, from 5.1 to 10.8). The least-squares regression line predicting dissolved oxygen from temperature is $\hat{y}=13.2-0.30x.$ The purpose of this linear model is to summarize the linear association and predict typical dissolved oxygen for temperatures in the observed range. Which interpretation of the model is correct?
A coach uses regression to predict a runner's 5K time in minutes ( $y$ ) from weekly training miles ( $x$ ). The coach claims the slope is negative (more miles leads to faster times). A 98% confidence interval for the slope is $(-0.40,\ 0.05)$ minutes per mile. Is the claim supported by the confidence interval?
What does this indicate about that specific data point?
A teacher investigates whether time spent on a new online practice system is related to students' quiz scores. From a random sample of 35 students, the teacher records minutes spent practicing (explanatory variable $x$ ) and quiz score out of 20 (response variable $y$ ) and fits a least-squares regression line predicting score from minutes. The teacher's claim is that there is some linear relationship (slope not equal to 0). Which hypotheses are appropriate for testing this claim about the population slope?
A teacher suspects a student is not truly guessing on a 50-question True/False quiz. The student's answers show many short runs, but also two runs of 7 identical answers (seven T's in a row and later seven F's in a row). Under random guessing, you'd expect about half T and half F overall, with occasional longer runs appearing by chance. Is this pattern consistent with random behavior?
How many more students chose Summer as their favorite season than chose Winter?
A city planner wants to estimate the mean daily water use (in gallons) per household in a city. A random sample of 100 households is selected, and a 99% confidence interval for the population mean daily water use is calculated as (286, 314) gallons. Which interpretation is correct?

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