Practice Test 68 - AP Statistics

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

A city health department is testing whether a text-message reminder increases flu vaccination rates. The explanatory variable is reminder type (text-message reminder vs. no reminder), and the response variable is whether each person gets vaccinated within 30 days. The department identifies 1,000 residents from clinic records and randomly assigns 500 to receive texts and 500 to receive no texts. Which statement is most accurate about conclusions from this study?
A manufacturer tests whether the mean lifetime of a new battery exceeds 10 hours. They run a test with $H_0: \mu=10$ versus $H_a: \mu>10$ at $\alpha=0.01$ . The result is not statistically significant, so they conclude there is not enough evidence that the mean lifetime exceeds 10 hours and they keep the old design. In reality, the true population mean lifetime of the new battery is $\mu=10.8$ hours. Which type of error was made?
To estimate the proportion of all registered voters in a state who plan to vote in the next election, a polling organization calls landline phone numbers generated from a directory of landline listings. Cell-phone-only households are not included in the calling list. Which issue most threatens the validity of the poll's estimate?
An online retailer runs an A/B test on a sample of site visitors to see whether a new checkout design increases the proportion of completed purchases. Leaders will roll out the design if the test suggests an improvement. If the inference is wrong, the company could lose revenue by rolling out a harmful design or miss revenue by not adopting a beneficial one. Why is it important to consider potential error when making the rollout decision based on this test?
To compare two fertilizers, a researcher repeatedly takes an independent random sample of $n_1=10$ plants grown with Fertilizer A and $n_2=10$ plants grown with Fertilizer B, then records the mean height for each sample and computes $\bar{x}_A-\bar{x}_B$ . Suppose the population of heights for each fertilizer is strongly right-skewed, with no extreme outliers. Which statement is correct about the sampling distribution of $\bar{x}_A-\bar{x}_B$ ?
A retail company A/B tests a new checkout design on a sample of website visitors and finds evidence of a higher purchase rate. The company considers rolling it out to all users immediately. Why is it important to consider potential error in this inference, given that a rollout could either increase revenue or unintentionally reduce sales for many customers?
A fitness app company wanted to compare two reminder messages. They randomly assigned 400 current users to receive either Message A or Message B for 2 weeks. At the end, 62% of users assigned to A met a weekly step goal, compared with 55% assigned to B. Which conclusion is supported by the data?
A call center manager monitors the next 40 incoming calls. A success is a call that is resolved without being transferred, and historically the probability of resolution without transfer is $0.63$ for each call (assume independence). Which values of $n$ and $p$ correctly model the number of successes using a binomial distribution?
A public health official claims that at most 10% of households in a county have elevated radon levels. A random sample of 180 households is tested, and 27 have elevated radon (so $\hat{p}=0.15$ ). Which hypotheses are appropriate for testing whether the true population proportion $p$ is higher than the official's claim?
A factory fills exactly 60 cereal boxes on a line. A box is a success if its weight is at least the labeled weight; otherwise it is a failure. The line is known to drift over time, so the probability a box meets the labeled weight is higher early in the hour and lower later in the hour. Does this meet binomial conditions for modeling the number of successes among the 60 boxes?
A fitness coach models resting heart rate (beats per minute) as a function of weekly running mileage using data from a random sample of 28 clients. A 90% confidence interval for the slope is $(-0.90,\ -0.10)$ bpm per mile. Which interpretation is correct?
A basketball player takes 25 free throws in practice. The makes (M) and misses (X) in order are: M M X M X M M M X M X M M X M M M X M M X M X M M. Under random variation in performance you might see some short streaks of makes or misses, but not a strict rule. Is this pattern consistent with random behavior?
A restaurant chain claims that 70% of customers rate their experience as "satisfied." A random sample of 80 customers found 52 satisfied. A one-sample proportion test was performed at $\alpha=0.05$ with $H_0: p=0.70$ versus $H_a: p\ne 0.70$ . The $p$ -value was 0.29, so the manager failed to reject $H_0$ . Which conclusion is appropriate?
A wildlife agency estimates the proportion of an endangered bird species that survived the winter using a random sample of tracking tags. The agency will decide whether to impose stricter habitat protections if the sample suggests survival fell below a critical level. If the inference is wrong, protections could be imposed unnecessarily (affecting land use) or needed protections could be delayed (risking population decline). Why is it important to consider potential error when making this decision from the sample data?
A hospital studies the waiting time (in minutes) for patients in the emergency department. The population distribution is strongly right-skewed because a few patients wait a very long time. A random sample of $n=70$ patients is selected, and the mean waiting time is computed. Why is the sampling distribution of $\bar{x}$ approximately normal?
A student council wants to study whether students at a large high school support a new policy requiring ID badges. The council plans to stand outside the cafeteria during lunch for two days and ask passing students to complete a short anonymous survey about support or opposition. The research question is: "What proportion of all students at this high school support the ID badge policy?" Which aspect is most important to address before collecting data?
A teacher models exam score ( $y$ ) from number of practice problems completed ( $x$ ) for 40 students. The teacher claims that each additional problem increases the mean exam score by between 0.5 and 1.0 points. A 90% confidence interval for the slope is $(0.62, 0.95)$ points per problem. Is the claim supported by the confidence interval?
A hospital summarizes the number of hours patients spent in the emergency department for 55 visits. The five-number summary (hours) is: minimum $0.5$ , $Q_1=1.2$ , median $2.0$ , $Q_3=3.6$ , maximum $7.5$ . A boxplot is made from these values. Which feature is consistent with the summary statistics?
A coffee shop measures the wait time (in minutes) for 70 customers during the morning rush. The five-number summary is: min $=2$ , $Q_1=4$ , median $=6$ , $Q_3=9$ , max $=20$ . A boxplot is constructed using these values (no outliers marked). Which feature is consistent with the summary statistics?
A university newspaper reports that 70% of students approve of a new campus policy. A student group suspects the approval rate is actually lower. In a random sample of 120 students, 76 approve (so $\hat{p}=0.633$ ). Which hypotheses are appropriate for testing the student group's suspicion about the population proportion $p$ ?

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