Practice Test 81 - AP Statistics

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

A state agency randomly sampled 1,000 residents to estimate the proportion $p$ of all residents in the state who have access to high-speed internet at home. In the sample, 790 reported having access. A 95% confidence interval for $p$ is $(0.76,\ 0.82)$ . Which interpretation is correct?
A city council member claims that 55% of city residents support a proposed recycling ordinance. A simple random sample of 400 residents is taken, and each resident is asked whether they support the ordinance (Yes/No). The council member wants to test whether the true support proportion differs from 55%. Which inference procedure is most appropriate?
A hospital compares mean length of stay (days) for patients receiving a new discharge protocol (New) versus the old protocol (Old). A 98% confidence interval for $\mu_{New}-\mu_{Old}$ is $(-1.9,\ -0.4)$ . The hospital claims the new protocol reduces mean length of stay. Is the claim supported by the interval?
A city counts the number of potholes reported, $X$ , on a randomly selected street segment in a month. The distribution is discrete with mean $\mu_X=4.1$ potholes and standard deviation $\sigma_X=2.3$ potholes. Which interpretation of the mean is correct?
A company tests two website designs for the proportion of visitors who make a purchase: Design 1 and Design 2. A 90% confidence interval for the difference $p_1 - p_2$ is $(-0.02, 0.07)$ . A designer claims, "Design 1 leads to a higher purchase rate than Design 2." Is the claim supported by the confidence interval?
An engineer wants to estimate the mean tensile strength (in MPa) of a type of cable. She randomly tests 12 cables and constructs a 95% confidence interval for the population mean tensile strength: (510, 545) MPa. Which interpretation is correct?
A jar contains many marbles, and a single marble is selected at random and then replaced. The sample space for one draw is $\{\text{Red},\text{Blue},\text{Green}\}$ . The event of interest is drawing a green marble, and the model gives $P(\text{Green})=0.10$ . Which statement correctly describes the probability $0.10$ ?
A city health department randomly selects 250 adults from its list of registered residents and asks whether they have received a flu shot this year. Of those sampled, 148 say "yes." Which conclusion is supported by the data?
A school district samples 120 students and estimates that 18% would qualify for free tutoring under a new academic-support program. Funding decisions must be made now: if the district underestimates need, some students may go without support; if it overestimates, money may be diverted from other programs. Why is it important to consider potential error?
Two fertilizers are compared by measuring mean tomato yield (in pounds per plant). Fertilizer X had a sample mean yield of 6.4 and Fertilizer Y had a sample mean yield of 6.6. A 95% confidence interval for the difference in population means, defined as $\mu_X-\mu_Y$ , is $(-0.5, 0.2)$ . A gardener claims, "Fertilizer X produces a lower mean yield than Fertilizer Y." Is the claim supported by the confidence interval?
For the population of newborns at a hospital, birth weights are approximately Normal with mean $\mu=3.4$ kg and standard deviation $\sigma=0.5$ kg. The neonatal unit marks the interval 2.9 kg to 3.9 kg as "typical range." Which statement about the marked interval is correct?
A researcher studies whether preferred study environment is related to class year. A random sample of students is classified by class year (Freshman, Sophomore, Junior, Senior) and preferred environment (Quiet, Background Music, Group Setting). The data are summarized in a $4\times 3$ two-way table of counts. The researcher wants to know if class year and preferred environment are associated in the population. Which inference procedure is most appropriate?
A teacher is curious whether the class period affects quiz performance. For each student in Algebra I, the teacher records class period (1st, 2nd, 3rd, or 4th) and quiz score (out of 20 points). The goal is to compare quiz scores across class periods. Observational units are the students. Which classification is correct?
A botanist measured sunlight exposure ( $x$ , hours/day, from 3 to 11) and plant height after 6 weeks ( $y$ , cm) for 10 plants of the same species. The least-squares regression line predicting height from sunlight is $\hat{y}=12.5+2.8x$ . The purpose of this linear model is to summarize the linear association and predict typical height for sunlight values in the observed range. Which interpretation of the model is correct?
A biologist samples 18 wetlands and records water pH ( $x$ ) and frog call rate ( $y$ , calls per minute). A least-squares regression line is used to predict call rate from pH. A 90% confidence interval for the true slope is $(-3.8,\ 0.6)$ calls per minute per pH unit. Which interpretation is correct?
A streaming service wants to estimate the proportion of its subscribers who watched a new series in the first month. It takes two independent random samples from the same subscriber population. In Sample 1 (n = 300), 42% watched the series; in Sample 2 (n = 300), 46% watched the series. The sampling procedure was identical. Why might the sample results differ?
A teacher compares the mean score on a quiz for students who used an online practice tool versus students who did not. A random sample of 24 students who used the tool had a mean score of 82.5, and a random sample of 26 students who did not use the tool had a mean score of 78.9. The research claim is that using the tool increases the mean quiz score. Which hypotheses are appropriate?
A librarian recorded the number of pages in each of 36 books returned on a particular day, using the page count printed in each book. The dotplot below shows the distribution of page counts. Which feature of the distribution is most evident?
A wildlife biologist summarized the lengths (in centimeters) of 65 fish caught in a lake. The summaries were: mean $=24.5$ cm, median $=24.0$ cm, SD $=4.0$ cm, $Q_1=22.0$ cm, $Q_3=27.0$ cm, minimum $=15$ cm, maximum $=33$ cm (five-number summary: $15, 22, 24, 27, 33$ ). Which interpretation is correct?
A gym owner believes members spend an average of $\mu=45$ minutes per visit. A random sample of 60 visits is recorded, and a one-sample $t$ test is conducted with $H_0:\mu=45$ and $H_a:\mu>45$ at $\alpha=0.10$ . The p-value is 0.27. What conclusion is appropriate?

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