Practice Test 18 - AP Statistics

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

Two online stores want to compare the proportion of orders delivered on time. From recent random samples, Store X had 255 on-time deliveries out of 300 orders and Store Y had 228 on-time deliveries out of 300 orders. A 95% confidence interval for $p_X - p_Y$ is $(0.01,\ 0.19)$ . A manager claims Store Y has a higher on-time delivery rate than Store X. Is the claim supported by the confidence interval?
A website claims its "random quote" button selects from many quotes uniformly at random. A user clicks the button 30 times and records whether the quote begins with the word "The" (T) or not (N). The sequence is: T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T. The user suspects the button is not behaving randomly. Is the pattern consistent with random behavior?
A streaming service wants to estimate the proportion of all subscribers who would recommend the service. After a user finishes watching a show, a pop-up asks, "You loved this service, right? Would you recommend us to a friend?" and records answers from those who click one of the options. Which issue most threatens the validity of the results?
A school nurse recorded the number of minutes 60 students slept the night before a standardized test. The summary statistics were: mean $= 420$ min, median $= 435$ min, standard deviation $= 55$ min, five-number summary $( \min, Q_1, \text{Med}, Q_3, \max) = (290, 390, 435, 465, 520)$ , and IQR $= 75$ min. Which interpretation is correct?
To estimate the population mean height $\mu$ of all students at a university, a student selects an SRS of 30 students and measures height, but rounds every measurement to the nearest 2 inches before computing the sample mean $\bar{x}$ from the rounded values. She reports this rounded-data mean as the point estimate for $\mu$ . Which statement describes whether the estimate is biased?
A school district says that 65% of students ride the bus. A statistician repeatedly selects many random samples of $n=80$ students and calculates $\hat p$ each time. Which statement about the sampling distribution is correct?
A business analyst tests whether advertising spending ( $x$ , thousands of dollars) predicts weekly sales ( $y$ , thousands of dollars) for 16 weeks. A regression of sales on ad spending is fit, and a slope test is performed with $H_0: \beta_1=0$ versus $H_a: \beta_1>0$ . The reported one-sided p-value is 0.008, and at $\alpha=0.05$ the analyst rejects $H_0$ . What conclusion is appropriate?
A public health team is comparing whether the distribution of vaccination status (Up to date, Not up to date) is the same across four clinics (A, B, C, D). They take separate random samples of patients from each clinic during the same week and record vaccination status. The two-way table shows the results. Which chi-square test is appropriate, and what are the correct hypotheses? Note: Multiple groups (clinics) with one categorical response.
Daily low temperatures in a city during January are approximately Normal with mean $\mu=20^\circ\!F$ and standard deviation $\sigma=6^\circ\!F$ . Without calculating probabilities, which comparison is supported by the fact that the Normal curve is highest at the mean and decreases as you move away from the mean?
A factory records the weight of cereal in a box as $W$ ounces and the weight of the empty box as $B$ ounces. Assume $W$ and $B$ are independent with $\mu_W=18.2$ , $\sigma_W=0.4$ , $\mu_B=1.1$ , and $\sigma_B=0.1$ . Let $F=W+B$ be the total shipping weight. Which statement about $F$ is correct?
Based on this probability distribution, which conclusion is most appropriate?
A water utility claims the mean household water use is $\mu=320$ gallons per day. A random sample of households is taken and a 98% confidence interval for $\mu$ is $(300,\ 315)$ gallons per day. Is the claim supported by the confidence interval?
A teacher models final course grade (percent) as a linear function of number of classes missed for a random sample of students. A 95% confidence interval for the slope is $(-3.5,\ -1.2)$ . Which interpretation is correct?
A bank analyzed the amounts of 70 mobile check deposits (in dollars) made in one week. The summaries were: mean $=410$ , median $=250$ , SD $=520$ , five-number summary $(20,\ 120,\ 250,\ 480,\ 3200)$ , and IQR $=360$ . Which interpretation is correct?
A fitness researcher randomly samples 12 adults and measures their resting heart rates (beats per minute). A one-sample $t$ interval is used to estimate the population mean resting heart rate, producing a 95% confidence interval of $(66.4,\ 74.9)$ . Which interpretation is correct?
A shipping company claims that the mean delivery time for a certain route is at least 2.5 days. A competitor believes the mean delivery time is actually less than 2.5 days. A random sample of $n=45$ deliveries on that route is selected, and the sample mean delivery time is $\bar{x}=2.3$ days. Which hypotheses are appropriate for a test of the population mean delivery time, $\mu$ ?
A store manager tracks the last digit of each of 40 customer receipts (0–9). If the last digit is generated by a random process, you would expect the digits to be fairly even overall with some natural variation and no obvious restriction. The manager notices the last digit is always even (0,2,4,6,8), never odd. Is the pattern consistent with random behavior?
A school district wants to estimate the mean number of minutes per day that all middle school students in the district spend on homework. The district selects 4 of its 12 middle schools based on which principals respond first to an email request to participate, then surveys all students in those 4 schools. Which issue most threatens the validity of the estimate for the entire district?
A machine fills bottles, and a technician inspects bottles one at a time until finding the first bottle that is underfilled. Each inspection results in either "underfilled" or "not underfilled." Assume the probability a bottle is underfilled is constant over time and inspections are independent. The technician wants to model the number of bottles inspected until the first underfilled bottle. Why is a geometric model appropriate?
An environmental scientist measures mean nitrate concentration (mg/L) in water samples from two rivers. A random sample of $n=18$ samples from River A had mean $\bar{x}=6.4$ mg/L, and a random sample of $n=20$ samples from River B had mean $\bar{x}=5.7$ mg/L. The claim is that River A has a higher population mean nitrate concentration than River B. Which hypotheses are appropriate?

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