Practice Test 86 - AP Statistics

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

In a lab, $M$ is the measured mass (in grams) of a sample and $E$ is the measurement error (in grams), where $E$ can be positive or negative. Assume $M$ and $E$ are independent with $\mu_M=50.0$ , $\sigma_M=0.8$ , $\mu_E=0.0$ , and $\sigma_E=0.3$ . The corrected mass is defined as $C=M-E$ . Which statement about $C$ is correct?
A researcher compares the proportion of plants that survive under two fertilizers. Fertilizer A: random sample of $n_A=40$ plants; Fertilizer B: independent random sample of $n_B=40$ plants. The statistic is $\hat{p}_A-\hat{p}_B$ . Consider the condition for using a normal approximation for the sampling distribution of $\hat{p}_A-\hat{p}_B$ . Which statement is correct?
A teacher compares mean quiz scores (out of 20) for students who used paper flashcards versus a digital flashcard app. A random sample of $n=33$ paper users had mean $\bar{x}=15.2$ , and a random sample of $n=35$ app users had mean $\bar{x}=16.1$ . The claim is that app users have a higher population mean quiz score than paper users. Which hypotheses are appropriate?
An engineering team wants to test whether two materials (Material X vs Material Y) produce different average breaking strengths. The testing machine warms up over time, potentially affecting measured strength, so the team plans to test 20 samples total in one day. They can randomize the order of tests, and each sample can be tested only once (it breaks). Which experimental design is most appropriate?
Two brands of batteries are tested. Let $p_A$ be the true proportion of Brand A batteries that last at least 10 hours, and $p_B$ for Brand B. A 95% confidence interval for $p_B-p_A$ is $(-0.09,\ 0.02)$ . A consumer claims, "Brand B has a higher proportion lasting at least 10 hours than Brand A." Is the claim supported by the interval?
A researcher repeatedly takes independent random samples from two populations to compare average daily screen time. Each repetition uses $n_1=15$ teens from City 1 and $n_2=15$ teens from City 2, computing $\bar{x}_1-\bar{x}_2$ . The population distributions are strongly right-skewed, but both have finite means and standard deviations. Which statement about the sampling distribution of $\bar{x}_1-\bar{x}_2$ is correct?
A hospital tracks whether each arriving patient is admitted (A), discharged (D), or transferred to another facility (T). For a randomly selected arriving patient on a typical weekday, the sample space is $\{A, D, T\}$ . Based on long-run hospital records, the probability of transfer is $P(T)=0.12$ . Which statement correctly describes the probability $0.12$ in this context?
A runner tests two shoe models for mean 5K time (in seconds) among similar runners. The claim is that Model A produces a faster mean time than Model B. A 95% confidence interval reported is for $(\mu_{B}-\mu_{A})$ and equals $(12,\ 48)$ . Is the claim supported by the confidence interval?
A fitness app company compared the proportion of users who remain active after 30 days for two independent random samples: 92 of 160 users who received daily reminders stayed active, and 75 of 155 users who did not receive reminders stayed active. A two-proportion $z$ test at $\alpha=0.10$ tested $H_0: p_R=p_N$ versus $H_a: p_R>p_N$ , where $p_R$ is the true active-after-30-days proportion with reminders and $p_N$ is the true proportion with no reminders. The p-value was 0.07. What conclusion is appropriate?
A factory's long-run defect rate for a certain part is about 2%. A quality engineer randomly inspects 500 parts from one day's production and finds 20 defective (4%). The engineer wants to know whether 4% is surprising for $n=500$ if the true defect rate is 2%, considering typical sampling variability. Is the result unexpected?
A marketing team samples 22 weeks, recording $x$ = number of promotional emails sent (in thousands) and $y$ = weekly revenue (in thousands of dollars). The regression of revenue on emails gives a 95% confidence interval for the population slope $\beta$ of $(0.0,\ 2.5)$ (with the lower endpoint rounded to 0.0). Which interpretation is correct?
A pharmacy chain samples 60 stores and estimates the mean wait time for prescriptions to decide whether to implement a new staffing plan. The plan is expensive, but long wait times can reduce customer satisfaction and health outcomes. Why is it important to consider potential error when using the sample mean wait time to make this decision?
A nurse suspects a pain-relief button is malfunctioning. Each press should randomly deliver either a standard dose (S) or a slightly reduced dose (R) with fixed probabilities. Over 80 presses, the sequence includes several runs of 5–6 S's in a row, and one run of 8 S's in a row, but R's still occur throughout. Under random behavior, you might see occasional long runs, and runs alone don't prove a problem. Is the pattern consistent with random behavior?
When describing a distribution of quantitative data that is strongly skewed with several outliers, which measures of center and variability are generally most appropriate to use?
The amount of caffeine (mg) in a certain brand of coffee has population mean $\mu=95$ mg and population standard deviation $\sigma=20$ mg. The distribution of individual caffeine amounts is unknown. A student repeatedly takes random samples of size $n=4$ cups and computes $\bar{x}$ . Which statement about the sampling distribution of $\bar{x}$ is correct?
A city collected the number of text messages sent yesterday by a random sample of 28 high school students. The dotplot below displays the distribution. Which statement best describes the distribution?
A phone battery model has a mean lifetime of $\mu=11$ hours under a standard test. A technician repeatedly selects random samples of $n=25$ batteries and computes the sample mean lifetime $\bar{x}$ . Assume the sampling distribution of $\bar{x}$ is approximately normal. Which statement about the sampling distribution is correct?
A sports analyst compares average free-throw percentages for two independent teams. In each repetition, the analyst takes an independent random sample of $n_1=20$ players from Team 1 and $n_2=80$ players from Team 2 and computes $\bar{x}_1-\bar{x}_2$ . Assume the population distributions of player percentages are roughly symmetric with standard deviations $\sigma_1$ and $\sigma_2$ . Which statement is correct about the shape of the sampling distribution of $\bar{x}_1-\bar{x}_2$ ?
A tech company claims that 10% of its users enable two-factor authentication (2FA). A random sample of 600 users found 78 had enabled 2FA. A one-sample $z$ test for a population proportion was conducted with hypotheses $H_0: p=0.10$ and $H_a: p\ne 0.10$ at $\alpha=0.05$ . The test resulted in a $p$ -value of 0.031, so $H_0$ was rejected. Which conclusion is appropriate?
A financial analyst models the relationship between years of work experience ( $x$ , years) and annual salary ( $y$ , dollars) for a random sample of 45 employees at a large company. A 92% confidence interval for the population slope is $ (1500, 4200) $ dollars per year of experience. Which interpretation is correct?

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