Practice Test 37 - AP Statistics

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

A city's mayor claims that more than 60% of residents are in favor of a new public park initiative. To test this claim, an independent polling agency conducts a survey of a random sample of residents. Let $p$ represent the true proportion of residents who favor the initiative. Which of the following are the correct null and alternative hypotheses?
A researcher wants to test whether listening to music while studying improves memory recall. She recruits 80 students from a dormitory. She pairs students by similar GPA, then within each pair randomly assigns one student to study vocabulary words for 20 minutes with instrumental music and the other to study in silence. Afterward, both take the same recall quiz. Which conclusion is justified based on the design?
A genetics model predicts offspring phenotypes in a 3-category ratio of 1:2:1 (Type A, Type B, Type C). A researcher records 160 offspring: A=35, B=92, C=33. A chi-square goodness-of-fit test is conducted with $H_0$ : the population follows the 1:2:1 distribution. The test produces $p$ -value = 0.18. Observed vs. Expected counts (under $H_0$ ): - Type A: Observed 35, Expected 40 - Type B: Observed 92, Expected 80 - Type C: Observed 33, Expected 40 What conclusion is appropriate at $\alpha=0.05$ ?
A phone manufacturer claims its new battery lasts an average of 10 hours under a standardized test. A class expects that a random sample of 5 phones will average close to 10 hours. They test 5 phones and get a sample mean of 8.9 hours. Is this result unexpected, considering variability in sample means when the sample size is only $n=5$ ?
A student takes 40 practice problems and records whether each answer is correct on the first try. A success is "correct," and exactly 40 problems are attempted, but the student gets progressively better, so the chance of success increases. Does this meet binomial conditions?
A streaming service looked at whether users have a premium subscription (Premium/Standard) and whether they watch documentaries at least weekly (Yes/No). The purpose is to compare the weekly-documentary rates for premium vs standard users using conditional proportions. Which comparison is supported by the data? Counts: Premium: Yes 90, No 60 (Total 150). Standard: Yes 80, No 120 (Total 200).
A materials scientist investigates whether the percentage of carbon in steel ( $x$ ) predicts tensile strength in MPa ( $y$ ). The scientist claims that increasing carbon percentage increases tensile strength in the population over the tested range. Which hypotheses are appropriate for testing this claim about the slope of the population regression line?
A fitness center compared the proportion of members who renew their membership after one year under two pricing plans. In a random sample of 180 members on Plan X, 117 renewed; in a random sample of 200 members on Plan Y, 110 renewed. A two-proportion $z$ test was conducted for $H_0: p_X=p_Y$ versus $H_a: p_X>p_Y$ , and the p-value was $0.012$ . Using $\alpha=0.05$ , what conclusion is appropriate?
A game company claims that a spinner lands on 6 sections with probabilities (in order) 0.10, 0.15, 0.20, 0.20, 0.20, 0.15. A consumer group spins the spinner 300 times and records the counts shown in the table. A chi-square goodness-of-fit test is conducted for $H_0$ : the spinner follows the claimed probabilities vs. $H_a$ : it does not. The p-value is 0.003. What conclusion is appropriate at the $\alpha=0.05$ level? Observed/Expected counts and p-value: - p-value = 0.003
A machine fills 50 bottles, and for each bottle the manager records whether it is underfilled (below the minimum). A success is "underfilled," and exactly 50 bottles are checked in a row. The machine's settings stay constant during the checks. Does this meet binomial conditions?
A company wants to compare whether customers from two different regions (Region 1 and Region 2) have the same distribution of preferred customer-service contact method (Phone, Email, Chat, In-person). Independent random samples of customers are taken from each region. The results are shown in a table. Which chi-square test is appropriate, and what are the correct hypotheses? State clearly whether this is one sample or multiple groups.
A sports scientist wanted to determine whether a new stretching routine improves 100-meter sprint times for members of a high school track team. All 40 athletes on the team participated. The scientist randomly assigned 20 athletes to use the new stretching routine for four weeks and 20 athletes to continue their usual stretching. After four weeks, each athlete ran a timed 100-meter sprint. Which conclusion is justified based on the design of this study?
A fitness app claims that the mean number of steps per day for its users is more than $\mu=8000$ . A random sample of 50 users is selected and a one-sample $t$ test is performed with $H_0:\mu=8000$ versus $H_a:\mu>8000$ at $\alpha=0.05$ . The p-value is 0.006. What conclusion is appropriate?
A school compares mean time (in minutes) spent on homework per night for students in two programs: Program A and Program B. The sample mean for Program A was 78 minutes and for Program B was 72 minutes. A 95% confidence interval for the difference in population means, defined as $\mu_A-\mu_B$ , is $(1, 11)$ minutes. A student claims, "Students in Program A spend more time on homework on average than students in Program B." Is the claim supported by the confidence interval?
A city engineer measured the lengths (in seconds) of all red lights at a set of 40 intersections in a neighborhood (population: those 40 red-light durations). The five-number summary is: min $=35$ , $Q_1=42$ , median $=50$ , $Q_3=58$ , max $=90$ . A boxplot is constructed. Which feature is consistent with the summary statistics?
A city council member claims that a majority of city residents support building a new public park. To test this, a random sample of 200 residents is surveyed and 118 say they support the park. A one-sample $z$ test for a population proportion is conducted at significance level $\alpha=0.05$ with hypotheses $H_0:p=0.50$ and $H_a:p>0.50$ . The test yields a $p$ -value of 0.12, so the decision is to fail to reject $H_0$ . Which conclusion is appropriate?
A city council member claims that more than 50% of residents support a proposed recycling ordinance. In a random sample of 200 residents, 118 said they support it. A one-sample $z$ test for a population proportion was conducted with $H_0: p=0.50$ versus $H_a: p>0.50$ at significance level $\alpha=0.05$ . The test produced a $p$ -value of 0.036, so the null hypothesis was rejected. Which conclusion is appropriate?
A real estate agent summarized the sale prices (in thousands of dollars) of 55 homes sold in a neighborhood last year. The summaries were: mean $=365$ , median $=340$ , SD $=90$ , five-number summary $(210,\ 295,\ 340,\ 400,\ 620)$ , and IQR $=105$ . Which interpretation is correct?
A student randomly selects 50 voters from a large city and records whether each voter supports a particular candidate. A success is "supports," and exactly 50 voters are surveyed. Does this meet binomial conditions to model the number of supporters?
A company wants to estimate the mean time (in minutes) that all customers nationwide spend on its website per visit. The analyst uses data from visits made on a single Tuesday between 1–3 P.M. Eastern Time and computes the mean time on site from those visits. Which issue most threatens the validity of generalizing to all customer visits?

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