Practice Test 15 - AP Statistics

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

An engineer compares mean battery life (hours) for two brands of rechargeable batteries. Independent random samples were tested (Brand X: $n=15$ ; Brand Y: $n=17$ ). A two-sample $t$ test for $\mu_X-\mu_Y$ was conducted with $H_0:\mu_X-\mu_Y=0$ and $H_a:\mu_X-\mu_Y>0$ . The p-value was 0.11. At $\alpha=0.05$ , what conclusion is appropriate?
A town wants to estimate the proportion of all registered voters who favor a proposed bond measure. A polling firm uses the town's voter registration list and selects a systematic sample by choosing a random starting point and then selecting every 20th name on the list. The list is ordered alphabetically by last name. Which statement best describes the sample representativeness?
A researcher flips a coin repeatedly until the first time it lands heads. A success is getting heads on a flip; a failure is tails. The researcher wants to model the number of successes. Does this situation meet the conditions for a binomial model?
A streaming service investigates the research question: "What percentage of all subscribers prefer watching with subtitles on?" The company randomly selected 1200 subscriber accounts from its full subscriber database and emailed one survey per selected account; 742 responded, and 55% of respondents reported preferring subtitles on. The company concluded that about 55% of all subscribers prefer subtitles on. Which statement explains whether the conclusion is valid?
A random number generator is supposed to produce digits 0–9 independently. A student records 40 outputs and notices this repeating block: 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 1, 4, 1. Under randomness you would expect no clear repeated cycle. Is the pattern consistent with random behavior?
A university wants to know whether class year (First-year, Sophomore, Junior, Senior) is related to preferred study location (Library, Dorm, Coffee shop). A single random sample of 240 students is surveyed, and each student reports both variables. The results are shown in the two-way table. Which test is appropriate, and what are the correct hypotheses? Note: One sample; two categorical variables.
A health clinic compares the proportion of patients who report side effects for two medications. Let $p_N$ be the true side-effect proportion for the new medication and $p_O$ for the older medication. A 98% confidence interval for $p_N-p_O$ is $(-0.01,\ 0.08)$ . A doctor claims, "The new medication causes side effects in a higher proportion of patients than the older medication." Is the claim supported by the interval?
An environmental scientist examines whether daily average temperature in °C ( $x$ ) predicts electricity usage in kWh ( $y$ ) during summer months. The scientist claims that hotter days lead to higher electricity usage in the population. Which hypotheses are appropriate for testing this claim about the slope of the population regression line predicting $y$ from $x$ ?
An environmental club measured daily high temperature ( $x$ , in °F) and the number of bottles of water sold at an outdoor booth ( $y$ ) for 15 days, with temperatures ranging from 60°F to 92°F. A least-squares regression line was found: $\hat{y} = -120 + 4.1x$ . The purpose of this linear model is to describe the relationship and predict typical sales for temperatures within the observed range. Which interpretation of the model is correct?
To compare mean systolic blood pressure for two independent groups, a clinic takes an SRS of $n_1=80$ patients who exercise regularly and an independent SRS of $n_2=20$ patients who do not. The statistic is $\bar{x}_1-\bar{x}_2$ . Assume both populations have the same standard deviation. Which statement is correct about the variability of the sampling distribution of $\bar{x}_1-\bar{x}_2$ ?
A city council uses a random sample survey to estimate support for a new tax that would fund wildfire prevention. The sample suggests a majority supports the tax, so the council plans to put it on the ballot. Why is it important to consider potential error in this inference, given that placing the measure on the ballot costs money and a failed measure could delay prevention efforts?
An environmental scientist models daily ozone level ( $y$ ) using daily high temperature ( $x$ ) in a city. The scientist claims there is a negative linear association, meaning the true slope is less than $0$ . A 90% confidence interval for the slope is $(-1.8,\ -0.4)$ (ozone units per degree). Is the claim supported by the confidence interval?
A researcher compared commute times (minutes) for employees who drive versus employees who take public transit. Five-number summaries are shown below. Which comparison is supported by the display? - Drive: min 10, $Q_1$ 18, median 25, $Q_3$ 35, max 55; no outliers - Transit: min 15, $Q_1$ 25, median 40, $Q_3$ 55, max 90; no outliers
A commuter's total travel time is the sum of two independent parts. Let $X$ be the time (in minutes) spent walking to the bus stop with $\mu_X=7$ and $\sigma_X=2$ . Let $Y$ be the time (in minutes) spent riding the bus with $\mu_Y=23$ and $\sigma_Y=6$ . Define $T=X+Y$ , the total commute time. Which statement about the combined variable is correct?
All data values are multiplied by 3. What happens to the boxplot's box length?
A restaurant chain wants to check whether the proportion of customers who rate their experience as "excellent" is still 0.60 after a menu change. A random sample of 180 customers found that 96 rated their experience as excellent. A one-sample $z$ test for a population proportion was conducted with $H_0: p=0.60$ versus $H_a: p\ne 0.60$ at significance level $\alpha=0.05$ . The test produced a $p$ -value of 0.022, so the null hypothesis was rejected. Which conclusion is appropriate?
A school district wants to know whether a new online homework system changes mean weekly math quiz scores. A random sample of students used the new system (group N) and another random sample used the old system (group O). A two-sample $t$ test was performed for $H_0: \mu_N-\mu_O=0$ versus $H_a: \mu_N-\mu_O>0$ . The test produced a p-value of 0.03. Using $\alpha=0.05$ , what conclusion is appropriate?
A university compares the proportion of applicants who accept an admission offer for two majors. Let $p_S$ be the true acceptance proportion for STEM offers and $p_H$ for Humanities offers. A 95% confidence interval for $p_H-p_S$ is $(-0.22,\ -0.05)$ . An advisor claims, "A higher proportion of students accept STEM offers than Humanities offers." Is the claim supported by the interval?
A public health researcher compares smoking rates in two cities. In a random sample of 160 adults from City X, 44 are current smokers. In a random sample of 140 adults from City Y, 54 are current smokers. The researcher's claim is that the proportion of smokers differs between the two cities. Which hypotheses are appropriate for testing this claim using a difference in two population proportions?
A university wants to estimate the proportion of all undergraduate students who own a bicycle. Two independent simple random samples of 150 undergraduates are taken from the same enrollment list. The first sample finds 38% own a bicycle; the second finds 44% own a bicycle. Why might the sample results differ?

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