Practice Test 31 - AP Statistics

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

A school principal wants to estimate the proportion of students at the school who eat breakfast every school day. She emailed a survey link to all 1800 students and used the first 300 responses received within 2 hours. Of those 300, 62% reported eating breakfast every school day. She concluded that "about 62% of all students at the school eat breakfast every school day." Which statement explains whether the conclusion is valid?
A consumer group tests the battery life of a sample of smartphones. The group's report states that the distribution of battery life is "roughly symmetric with a prominent peak around 12 hours." What does the term "prominent peak" signify in the description of this distribution?
A hospital compares patient wait times in two departments. Repeatedly, it takes an independent random sample of $n_1=100$ patients from the ER and $n_2=20$ patients from Urgent Care and computes $\bar{x}_{ER}-\bar{x}_{UC}$ . Which statement is correct about the sampling distribution of $\bar{x}_{ER}-\bar{x}_{UC}$ ?
A hospital administrator reviews exactly 25 patient records from last month. For each record, the administrator notes whether the patient was readmitted within 30 days (success) or not readmitted (failure). Because the 25 records are chosen randomly from a very large set of records, the administrator treats the selections as approximately independent. Does this meet the binomial conditions?
A health clinic recorded whether patients received a flu shot this season (Shot/No Shot) and whether they reported getting the flu (Flu/No Flu). The two-way table shows the results. Which comparison is appropriate for assessing whether getting the flu is associated with receiving a flu shot? Categorical variables: Flu shot status and Flu occurrence.
A nutrition label states that a certain brand of granola bars has a mean calorie content of $\mu=190$ calories per bar. A quality-control manager takes a random sample of 12 bars and performs a one-sample $t$ test: $H_0:\mu=190$ vs. $H_a:\mu\ne 190$ , at $\alpha=0.05$ . The p-value is 0.64. What conclusion is appropriate?
A nonprofit claims that fewer than 15% of donors give anonymously. A random sample of 350 donors is selected, and a 95% confidence interval for the true proportion of anonymous donors is $(0.14, 0.19)$ . Is the claim supported by the confidence interval?
A restaurant chain wants to estimate the proportion of all customers who are satisfied with a new menu. It prints a survey code on receipts, and customers can complete the survey online for a chance to win a $50 gift card. The chain summarizes results from the customers who chose to participate. Which issue most threatens the validity of using these results to represent all customers?
A teacher wants to know whether offering optional review sessions increases the proportion of students who pass the final exam. In one class section with review sessions, 52 of 80 students passed. In another section without review sessions, 61 of 100 students passed. The teacher's research claim is that the review sessions increase the pass rate. Which hypotheses are appropriate for testing the teacher's claim about the population proportions?
A hospital is considering adopting an AI tool that flags patients at high risk of sepsis. Administrators evaluate the tool using a study of a random sample of past patient records and plan to implement the tool if the study suggests it improves early detection. If the inference is wrong, the hospital could either miss true sepsis cases or overwhelm staff with false alarms. Why is it important to consider potential error when using the study results to decide whether to adopt the tool?
A city monitors the concentration of a pollutant (in parts per billion, ppb) at a location each day. The population mean daily concentration is $\mu=18$ ppb with population standard deviation $\sigma=7$ ppb, and the daily values can be quite variable. Each month, an analyst repeatedly selects random samples of $n=30$ days and computes the sample mean concentration $\bar{x}$ . Which statement about the sampling distribution of $\bar{x}$ is correct?
A school counselor collected data from 18 students on weekly hours of sleep ( $x$ ) and number of days absent in a semester ( $y$ ). A least-squares regression of $y$ on $x$ was fit, and a slope test was performed: $H_0: \beta_1=0$ vs. $H_a: \beta_1\ne 0$ . The computer output reported a negative estimated slope and a p-value of 0.012. Using $\alpha=0.05$ , the counselor rejected $H_0$ and concluded there is convincing evidence of a linear association between sleep and absences in the population of similar students. What conclusion is appropriate?
A university wants to determine whether the proportion of students who live on campus is the same across four class years (First-year, Sophomore, Junior, Senior). A random sample of 80 students from each class year is selected, and each student is recorded as living on campus (Yes/No). Which inference procedure is most appropriate?
A wildlife biologist claims that a certain species of bird nests in four habitat types in the following proportions: Forest 35%, Grassland 30%, Wetland 20%, and Urban 15%. The biologist observes $n=160$ nests and records the counts by habitat type shown in a table. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the claimed habitat distribution?
Which of the following statements provides the most complete description of a distribution of a quantitative variable?
A game involves drawing 3 cards without replacement from a standard 52-card deck. You win if you get at least 2 hearts. A student estimates the probability of winning by simulation: for each trial, the student shuffles a virtual deck, draws 3 cards, records whether the trial is a win, and repeats for 5000 trials. The simulation reports 820 wins. Which interpretation of the simulation results is correct?
A coffee shop manager wants to estimate the mean amount of time customers wait in line during the morning rush. A random sample of 25 mornings was selected, and the manager recorded the average wait time (in minutes) for customers on each sampled morning. A 90% confidence interval for the population mean wait time was calculated as $(3.2,\ 4.5)$ minutes. Which interpretation is correct?
A sports scientist compares mean resting heart rate for two populations: endurance athletes (A) and nonathletes (N). Independent random samples are taken, and a two-sample $t$ test for $\mu_A-\mu_N$ is performed with $H_0: \mu_A-\mu_N=0$ and $H_a: \mu_A-\mu_N<0$ . The p-value is 0.27. At the $\alpha=0.05$ level, what conclusion is appropriate?
A random sample of 200 customers at a grocery store found that 46 used a self-checkout lane. A 96% confidence interval for the true proportion $p$ of all customers at that store who use self-checkout is $(0.18,\ 0.28)$ . Which interpretation is correct?
A company compares mean battery life (hours) of phones with Battery Model X versus Model Y. Using independent random samples, a 92% confidence interval for $(\mu_X-\mu_Y)$ is $(-1.0,\ 3.4)$ . Which interpretation is correct?

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