Practice Test 94 - AP Statistics

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

A researcher compares the proportion of left-handed students in School 1 and School 2. A 99% confidence interval for the difference in proportions, defined as $p_1 - p_2$ , is $(0.00, 0.09)$ . The researcher claims, "School 1 has a higher proportion of left-handed students than School 2." Is the claim supported by the confidence interval?
A package locker system records how many delivery attempts are needed for a randomly selected package before it is successfully delivered. Let $X$ be the number of attempts, a discrete random variable with mean $\mu_X=1.35$ attempts and standard deviation $\sigma_X=0.60$ attempts. Which interpretation of the mean is correct?
A basketball player shoots 15 free throws during practice. A shot is counted as a make (success) or a miss (failure). The player's long-run free-throw percentage is 80%, and each shot is treated as independent with the same chance of success. Let $X$ be the number of made free throws. Which values correctly model this situation?
A biologist observes exactly 18 animal births in a population over a season. A birth is a success if the offspring is male and a failure otherwise. The biologist suspects the chance of a male birth differs for younger mothers versus older mothers, and the 18 births include a mix of ages. Does this meet binomial conditions?
A hospital administrator wants to check whether the mean wait time in the emergency room is less than 45 minutes after a new triage system is introduced. A random sample of 30 wait times is collected, and a one-sample $t$ test is run: $H_0:\mu=45$ vs. $H_a:\mu<45$ , with $\alpha=0.05$ . The p-value is 0.12. What conclusion is appropriate?
A clinic compares the proportion of patients who report side effects for two medications. In a random sample, 22 of 140 patients taking Drug S report side effects and 30 of 150 patients taking Drug T report side effects. A 98% confidence interval for $(p_S - p_T)$ is $(-0.12, 0.01)$ . Which interpretation is correct?
A public health official samples 26 neighborhoods and records the number of parks ( $x$ ) and the percentage of adults meeting weekly activity guidelines ( $y$ ). A least-squares regression line predicts $y$ from $x$ . A 92% confidence interval for the true slope is $(0.4,\ 2.1)$ percentage points per park. Which interpretation is correct?
Based on the information provided, what is the frequency of mixed-breed dogs admitted during that month?
A botanist uses least-squares regression to predict plant height ( $y$ , cm) from amount of fertilizer ( $x$ , grams) using a random sample of 20 plants grown under similar conditions. A 95% confidence interval for the population slope is $( -0.6, 1.4)$ cm per gram. Which interpretation is correct?
A company compares the proportion of customers who renew a subscription under two email campaigns. From Campaign 1, an SRS of $n_1=80$ customers is selected; from Campaign 2, an independent SRS of $n_2=320$ customers is selected. The statistic of interest is $\hat{p}_1-\hat{p}_2$ . Over many repetitions, the sampling distribution of $\hat{p}_1-\hat{p}_2$ is centered at $p_1-p_2$ and has standard deviation $\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}}$ . Which statement is correct?
A school district compared the proportion of students who passed an end-of-course exam after two different review programs. In a random sample of 200 students using Program A, 128 passed; in a separate random sample of 180 students using Program B, 99 passed. A two-proportion $z$ test was performed for $H_0: p_A=p_B$ versus $H_a: p_A\ne p_B$ , and the p-value was $0.006$ . Using $\alpha=0.05$ , what conclusion is appropriate?
A manufacturer claims that at least 95% of its light bulbs last more than 1,000 hours. A quality-control team tests a random sample of 80 bulbs and constructs a 99% confidence interval for the true proportion lasting more than 1,000 hours: $(0.93, 0.98)$ . Is the claim supported by the confidence interval?
A streaming service wants to estimate the proportion of its subscribers who watched at least one documentary in the last month. Two analysts each take an independent random sample of 400 subscribers from the same subscriber database. Analyst 1 finds 0.41 watched a documentary; Analyst 2 finds 0.45 watched a documentary. Why might the sample results differ?
A company compares delivery times (minutes) for two shipping methods. In repeated sampling, they take an independent random sample of $n_1=25$ deliveries using Method 1 and an independent random sample of $n_2=100$ deliveries using Method 2, then compute $\bar{x}_1-\bar{x}_2$ . Which statement is correct about the sampling distribution of $\bar{x}_1-\bar{x}_2$ ?
A restaurant manager believes that more than $20\%$ of customers order dessert. During a randomly selected set of $n=150$ customer orders, $39$ include dessert (so $\hat{p}=0.26$ ). Which hypotheses are appropriate?
A nonprofit organization states that 15% of households in a county have experienced food insecurity in the past year. A researcher thinks the true proportion is different from 15%. From a random sample of 400 households, 74 report food insecurity (so $ \hat{p}=74/400$). Which hypotheses are appropriate for a one-proportion $z$ test?
A nutritionist studies whether a new diet lowers mean LDL cholesterol. A random sample of 25 adults follows the new diet (D) and an independent random sample of 27 adults follows their usual diet (U). A two-sample $t$ test for $\mu_D-\mu_U$ uses $H_0: \mu_D-\mu_U=0$ and $H_a: \mu_D-\mu_U<0$ . The p-value is 0.006. At $\alpha=0.01$ , what conclusion is appropriate?
A basketball player shoots exactly 25 free throws during practice. A success is making the shot; a failure is missing. However, the coach records that the player's chance of making a free throw increases after every make because of confidence, and decreases after every miss because of frustration. Does this meet binomial conditions for modeling the number of made shots?
A jar of candies is advertised to contain colors in these population proportions: 30% Red, 25% Blue, 20% Green, 15% Yellow, 10% Orange. A student randomly samples 100 candies and records counts: Red 34, Blue 22, Green 19, Yellow 16, Orange 9. A chi-square goodness-of-fit test of $H_0$ : the population proportions match the advertisement gives $p$ -value = 0.86. Expected counts under $H_0$ are: Red 30, Blue 25, Green 20, Yellow 15, Orange 10. What conclusion is appropriate at $\alpha=0.05$ ?
A botanist compared the proportion of seeds that germinate under two types of light. In a random experiment, 45 of 80 seeds germinated under Light A and 56 of 90 seeds germinated under Light B. A 95% confidence interval for $p_A - p_B$ is $(-0.22,\ -0.01)$ . Which interpretation is correct?

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