Practice Test 40 - AP Statistics

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

A bottled water company states its bottles have a mean volume of $\mu=500$ mL. A regulator tests whether the mean differs from the label. A random sample of 20 bottles is measured, and a one-sample $t$ test is performed with $H_0:\mu=500$ versus $H_a:\mu\neq 500$ at $\alpha=0.05$ . The p-value is 0.0004. What conclusion is appropriate?
A nurse practitioner believes the mean resting heart rate of adult patients at her clinic differs from the national mean of 72 bpm. She records the resting heart rate (in bpm) for a simple random sample of 30 adult patients from her clinic during routine visits. Which inference procedure is most appropriate to test her claim about the population mean?
A coin is advertised as fair. A student flips it 30 times, expecting about 15 heads, but gets 22 heads. Assuming the coin is actually fair and flips are independent, is this result unexpected given natural variability in 30 flips?
A researcher studied pet ownership (Owns a pet or Does not own a pet) and whether a person reports daily stress as high (High/Not high). Use the conditional distribution approach to describe the relationship. Which comparison is appropriate?
A researcher studies the difference in mean resting heart rate between two groups: runners and nonrunners. She takes an independent random sample of $n_R=64$ runners and $n_N=49$ nonrunners and computes $\bar{x}_R-\bar{x}_N$ . Assume the population standard deviations $\sigma_R$ and $\sigma_N$ are fixed. Which statement is correct about how the standard deviation of the sampling distribution changes if both sample sizes are doubled?
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 cafeteria manager believes that students choose lunch options in the following proportions: 50% hot meal, 30% salad, 20% sandwich. On one day, a random sample of 200 students is observed: 86 choose hot meal, 70 choose salad, and 44 choose sandwich. Which inference procedure is most appropriate to evaluate whether the observed distribution matches the manager's stated proportions?
A principal expects that the average number of absences per student in a month is about 1.5 days. The principal takes a random sample of 40 students and finds a sample mean of 2.1 absence days. The expected behavior is a sample mean near 1.5, but the observed outcome is higher. Is this result unexpected, given the variability of sample means for a random sample of size 40?
A researcher recorded the distance from a city center ( $x$ , in miles) and the monthly rent for a one-bedroom apartment ( $y$ , in dollars) for 13 apartments, with distances ranging from 1 to 18 miles. A least-squares regression line is $\hat{y}=1850-42x.$ The purpose of this linear model is to summarize the linear association and predict typical rents for apartments within the observed distance range. Which interpretation of the model is correct?
For a certain species of fish in a lake, the mean weight is $\mu=2.4$ kg. A biologist repeatedly takes random samples of $n=4$ fish and calculates the sample mean weight $\bar{x}$ . Assume the sampling distribution of $\bar{x}$ is approximately normal. Which statement about the sampling distribution is correct?
A city randomly sampled 500 registered voters and found that 275 support a proposed public transit tax. A 90% confidence interval for the true proportion $p$ of all registered voters in the city who support the tax is $(0.52,\ 0.58)$ . Which interpretation is correct?
A public health analyst compares average systolic blood pressure for two independent groups. In each repetition, an independent random sample of $n_1=64$ adults from Group 1 and $n_2=64$ adults from Group 2 is taken, and the statistic $\bar{x}_1-\bar{x}_2$ is recorded. The analyst knows $\sigma_1=16$ and $\sigma_2=10$ , and both populations are approximately normal. Which statement is correct?
A consumer group wants to estimate the mean lifetime (in months) of a certain brand of rechargeable battery. A random sample of 15 batteries was tested to failure, and a 95% confidence interval for the population mean lifetime was computed as $(18.2,\ 24.6)$ months. Which interpretation is correct?
A company says that 33% of its emails are opened within 1 hour. A data analyst repeatedly takes many random samples of $n=150$ emails and computes $\hat p$ . Which statement about the sampling distribution is correct?
In a large city, 12% of adults have a gym membership, 20% take public transit to work, and 5% do both. Let Event A be "a randomly selected adult has a gym membership" and Event B be "the adult takes public transit to work." Which statement about Events A and B is correct?
A technology company claims that exactly 30% of its employees work remotely at least three days per week. A random sample of 160 employees finds that 58 do so (so $\hat{p}=0.3625$ ). Which hypotheses are appropriate for testing whether the true population proportion $p$ differs from the company's claim?
A city's public health department wants to estimate the proportion of all adult residents who received a flu shot this year. Investigators stood outside two large hospitals on weekday mornings for one week and asked every 5th person leaving the building whether they had received a flu shot. People who agreed were recorded as the sample. Which issue most threatens the validity of using this sample to estimate the citywide flu-shot proportion?
For a certain brand of lightbulb, lifetimes (in hours) of all bulbs produced are approximately Normal with mean $\mu=1200$ and standard deviation $\sigma=150$ . A lifetime of $x=900$ hours is marked. Which statement about the marked value is correct?
A website A/B test randomly assigns visitors to Version A or Version B. A log of the first 50 visitors shows the assignment pattern: A appears 25 times and B appears 25 times, but the order is highly regular—every 2 visitors assigned to A are followed by every 2 visitors assigned to B, repeating (A,A,B,B,A,A,B,B,…). Under random assignment, you'd expect roughly equal totals but not such a repeating block pattern. Is the pattern consistent with random behavior?
A streaming service claims that 60% of its subscribers watch at least one documentary each month. A market analyst believes the true proportion is less than 60%. In a random sample of 150 subscribers, 81 report watching at least one documentary (so $ \hat{p}=81/150$). Which hypotheses are appropriate?

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