Practice Test 6 - AP Statistics

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

A school counselor wants to estimate the probability that, in a randomly selected group of 5 students from a large school, at least 2 have birthdays in the same month. To simulate, the counselor uses a random number generator that produces integers 1–12 (each equally likely) to represent birth months, generates 5 numbers for one trial, records whether at least one month appears at least twice, and repeats this process 1000 trials. The simulation produced 327 successes. Which interpretation of the simulation results is correct?
A dataset contains observations on the eye color of 80 individuals. If a frequency table is created for this data, which of the following must be true?
An online retailer wants to check whether the mean delivery time for a certain shipping option is 2 days. A random sample of 100 deliveries is selected, and a one-sample $t$ test is performed with $H_0:\mu=2$ versus $H_a:\mu\ne 2$ at $\alpha=0.05$ . The p-value is 0.58. What conclusion is appropriate?
A teacher compared the number of pages a student read in a week ( $x$ ) with the student's score on a reading quiz ( $y$ ) for 16 students. Pages ranged from 10 to 80. The least-squares regression line is $\hat{y} = 58 + 0.35x$ . The purpose of this linear model is to describe the linear association and predict typical quiz scores for page counts within the observed range. Which interpretation of the model is correct?
A school nurse believes that fewer than 30% of students get at least 8 hours of sleep on school nights. In a random sample of 120 students, 28 reported getting at least 8 hours. A one-proportion $z$ test was conducted for $H_0: p=0.30$ versus $H_a: p<0.30$ at $\alpha=0.10$ . The $p$ -value was 0.072, so the nurse rejected $H_0$ . Which conclusion is appropriate?
A city's transportation department claims that the mean time to clear a minor accident from a roadway is 30 minutes. A random sample of 16 minor accidents is observed, and the sample mean clearance time is $\bar{x}=33.5$ minutes. Which hypotheses are appropriate for testing whether the true mean clearance time $\mu$ is longer than the claimed value?
A student randomly guesses on exactly 15 multiple-choice questions, each with 4 answer choices. A success is guessing correctly; a failure is guessing incorrectly. Assume each guess is independent and the probability of a correct guess is the same on every question. Does this meet binomial conditions?
A sports medicine clinic wants to test whether a new stretching routine reduces hamstring tightness. The explanatory variable is the stretching routine (new routine vs. standard routine), and the response variable is hamstring flexibility measured by a sit-and-reach score after 4 weeks. Eighty volunteers are recruited from the clinic and then randomly assigned to follow either the new routine or the standard routine, with both groups meeting weekly with the same trainer. Which feature of this study allows the researchers to make a cause-and-effect conclusion about the stretching routine and flexibility?
To compare two fertilizers, an agronomist repeatedly selects independent random samples of plants: $n_1=50$ plants treated with Fertilizer A and $n_2=10$ plants treated with Fertilizer B. Plant growth (cm) is measured, and the statistic is $\bar{x}_A-\bar{x}_B$ . Assume both population distributions are roughly normal with standard deviations $\sigma_A=4$ and $\sigma_B=4$ . Which statement is correct about the sampling distribution of $\bar{x}_A-\bar{x}_B$ ?
A chef bakes 24 cookies and records whether each cookie is burnt. A success is "burnt," and exactly 24 cookies are evaluated, but cookies on the top rack burn more often than those on the bottom rack, and the batch includes both racks. Does this meet binomial conditions for one binomial model?
A public health official estimates the mean number of hours of sleep per night for adults in a county. A random sample of 45 adults is taken, and a 92% confidence interval for the population mean hours of sleep is $(6.4, 7.1)$ hours. Which interpretation is correct?
A city transit report claims that riders pay their fare using 55% card, 35% mobile app, and 10% cash. A random sample of 500 riders is observed, with counts shown in the table. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the report's claim? Observed counts table (n = 500): Card 292, Mobile app 158, Cash 50.
A psychologist compares mean reaction time (milliseconds) after drinking caffeinated tea versus decaffeinated tea. From independent random samples, a 98% confidence interval for $(\mu_{\text{caff}}-\mu_{\text{decaf}})$ is $(-25,\ -5)$ . Which interpretation is correct?
A school counselor wants to predict students' end-of-semester math exam scores ( $y$ , points) from the number of hours they reported studying in the final week ( $x$ , hours). Using data from students who studied between 0 and 12 hours, a least-squares regression line is fit: $\hat{y}=58+2.5x$ . The purpose of this linear model is to summarize the linear association and predict typical exam scores from study hours. Which interpretation of the model is correct?
A school district is investigating whether a higher proportion of students pass an algebra exam after using online tutoring compared with students who used in-person tutoring. In a random sample, 96 of 150 students using online tutoring passed, and 70 of 140 students using in-person tutoring passed. Which hypotheses are appropriate for a test of this claim?
A student investigates the relationship between engine size (liters) $x$ and highway fuel efficiency (mpg) $y$ for several cars and fits a least-squares regression line to predict mpg from engine size. The scatterplot with the fitted line is shown, and the goal is to use the model for prediction. Which statement about the regression line is correct?
A tech support center receives 25 calls in the next hour and records whether each call is resolved on the first attempt. A success is "resolved," and exactly 25 calls are observed. Assume call types vary widely, leading to different resolution probabilities by call. Does this meet binomial conditions?
A city official claims the mean commute time for residents is $\mu=25$ minutes. A random sample of residents yields a 95% confidence interval for $\mu$ of $(25,\,29)$ . Is the claim supported by the confidence interval?
A political analyst studies whether the amount of campaign spending in millions of dollars ( $x$ ) predicts vote share percentage ( $y$ ) for candidates. The analyst claims that higher spending is associated with higher vote share in the population. Which hypotheses are appropriate for testing this claim about the slope in the regression of $y$ on $x$ ?
A university administrator believes that more than 15% of students have taken at least one online course. A random sample of 400 students finds 78 who have taken an online course. A one-sample $z$ test for a population proportion is performed with $H_0: p=0.15$ and $H_a: p>0.15$ at $\alpha=0.05$ . The test yields a $p$ -value of 0.032, so $H_0$ is rejected. Which conclusion is appropriate?

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