Practice Test 26 - AP Statistics

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

A jar contains 30 beads, 6 of which are red. A student draws 10 beads without replacement and records whether each bead is red. A success is "red," and exactly 10 draws are made. Does this meet binomial conditions?
A discrete random variable $K$ represents the number of students absent from a particular class on a randomly chosen day. The distribution of $K$ has mean $\mu_K=1.1$ and standard deviation $\sigma_K=1.3$ . Which interpretation of the standard deviation is correct?
A sports scientist wants to see whether hydration plan affects time to run 5 km. Runners choose one of three hydration plans (Water only, Sports drink, No drink) and then run a 5 km course; the scientist records each runner's hydration plan and finishing time (in minutes). The observational units are runners, and the goal is to compare running times among plans. Which classification is correct?
A sports scientist compares the proportion of athletes who report reduced knee pain after 6 weeks using two training programs. In independent random samples, 58 of 100 athletes using Program P reported reduced pain and 49 of 100 using Program Q reported reduced pain. A two-proportion $z$ test for $H_0: p_P-p_Q=0$ versus $H_a: p_P-p_Q>0$ resulted in a p-value of $0.11$ . At $\alpha=0.05$ , what conclusion is appropriate?
A nutritionist compares mean sodium intake (mg/day) for adults following Diet A versus Diet B. Two independent random samples were taken (Diet A: $n=35$ ; Diet B: $n=33$ ). A two-sample $t$ test for $\mu_A-\mu_B$ used $H_0:\mu_A=\mu_B$ and $H_a:\mu_A<\mu_B$ . The p-value was 0.11. At the $\alpha=0.05$ level, what conclusion is appropriate?
A school compares the proportion of students who prefer online homework between two grades. In a random sample, 78 of 120 ninth-graders and 60 of 110 tenth-graders said they prefer online homework. A 95% confidence interval for the difference in population proportions $(p_9 - p_{10})$ is $(0.02, 0.20)$ . Which interpretation is correct?
When describing the distribution of a quantitative variable, why is it essential to address unusual features like outliers or gaps?
A manufacturer compares mean battery life (hours) for two brands of AA batteries: Brand X and Brand Y. Independent random samples of batteries are tested, and a two-sample $t$ test for $\mu_X-\mu_Y$ is performed with $H_0: \mu_X-\mu_Y=0$ and $H_a: \mu_X-\mu_Y>0$ . The p-value is 0.049. Using $\alpha=0.05$ , what conclusion is appropriate?
A school district wants to estimate the proportion of high school students who get at least 8 hours of sleep on a typical school night. Two different random samples are taken from the same district during the same month: Sample 1 surveys 120 students and finds 46% report at least 8 hours; Sample 2 surveys 120 different students and finds 54%. Why might the sample results differ?
A city planner recorded commute times (in minutes) for 60 workers who use public transit. The summaries were: mean $=41$ , median $=38$ , SD $=12$ , five-number summary $(15,\ 30,\ 38,\ 50,\ 85)$ , and IQR $=20$ . Which interpretation is correct?
A historian studies whether the year a building was constructed ( $x$ ) predicts the cost of annual maintenance in dollars ( $y$ ). The historian believes that newer buildings (larger $x$ ) tend to have lower maintenance costs in the population. Which hypotheses are appropriate for testing this claim about the population regression slope of $y$ on $x$ ?
An environmental scientist is studying a specific fish species in a small, isolated lake containing 120 of these fish. The scientist wants to test a hypothesis about the proportion of fish with a certain genetic marker. A simple random sample of 20 fish is captured. Why is a one-sample z-test for a proportion potentially inappropriate in this situation?
A health clinic wants to compare the distribution of appointment outcomes across two different reminder methods. Patients are randomly assigned to receive either a text reminder or a phone-call reminder. After one month, each patient's outcome is recorded as Kept, Canceled, or No-show. The two-way table summarizes the results. Which test is appropriate, and what are the correct hypotheses?
A teacher summarized the quiz scores (out of 20 points) for all students in one class. The five-number summary was: min $=4$ , $Q_1=11$ , median $=14$ , $Q_3=16$ , max $=19$ . A standard boxplot (with whiskers to the minimum and maximum) is made. Which feature is consistent with the summary statistics?
A consumer group repeatedly compares two brands of batteries by sampling. In each repetition, an independent random sample of $n_1=9$ batteries of Brand A and $n_2=9$ batteries of Brand B is tested for lifetime (hours), and $\bar{x}_A-\bar{x}_B$ is recorded. Assume both population lifetime distributions are normal with standard deviations $\sigma_A$ and $\sigma_B$ . Which statement is correct?
A quality-control inspector selects 20 light bulbs from a large shipment and records whether each bulb works when first turned on. A success is "the bulb works," and the inspector tests exactly 20 bulbs in the same way. Does this situation meet the conditions for using a binomial model to count the number of successes?
For a certain brand of lightbulbs, lifetimes (in hours) for individual bulbs have mean $\mu=1100$ and standard deviation $\sigma=250$ , and the distribution is strongly right-skewed. A store repeatedly selects many random samples of $n=64$ bulbs and computes the sample mean lifetime $\bar{x}$ . Which statement about the sampling distribution of $\bar{x}$ is correct?
A lab group measures the concentration of a solution (mol/L) and the reaction rate (mL/min). The scatterplot shows a strong positive linear association. One student suggests converting concentration from mol/L to mmol/L (multiplying by 1000). Which statement about correlation is correct?
A medical study compares mean systolic blood pressure (in mmHg) for patients taking Drug M versus patients taking a placebo. A random sample of 40 patients taking Drug M had a mean systolic blood pressure of 128 mmHg, and a random sample of 41 patients taking the placebo had a mean of 132 mmHg. The research claim is that Drug M lowers mean systolic blood pressure compared with placebo. Which hypotheses are appropriate?
A psychologist studies whether a 10-minute daily journaling routine reduces anxiety. She recruits 72 participants and measures anxiety score after 4 weeks. Participants are first grouped by baseline anxiety level (low, medium, high), and within each group, she randomly assigns half to journaling and half to no journaling. Which best describes why the psychologist grouped participants by baseline anxiety before random assignment?

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