AP Statistics Unit 3

At Central High School, 28% of the students are Freshmen, 26% are Sophomores, 24% are Juniors, and 22% are Seniors. The student manager of the school newspaper would like to conduct a survey to estimate the proportion of each class that plans to attend the upcoming Football game. She suggests surveying a random sample of 100 students, but specifically by selecting random samples of 28 Freshmen, 26 Sophomores, 24 Juniors, and 22 Seniors. Which of the following is a true statement about this sampling procedure?

• This is a simple random sample because students of every class have an equal chance of being selected.

• This is a cluster random sample because there are 4 groups of students that are to be selected.

• This is a convenience sample because only 100 students are surveyed, which is a manageable size.

• This is a stratified random sample because a separate random sample is selected from each class.

• Yes, because the difference between the sample proportion and the population proportion is 0.04, which is less than 0.05.

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CCSS.HSS.IC.B.3

A study is conducted to investigate whether customer satisfaction is greater among computer companies that offer tech support versus those that do not offer tech support. A random sample of 50 customers are selected from among those that purchased computers that offer tech support. A separate random sample of 40 customers are selected from among those that purchased computers that do not offer tech support.

The study found that the mean satisfaction rating was significantly greater among customers that purchased computers that offer tech support.

Which of the following is the best description of this study?

• An experiment using a completely randomized design.

• An experiment using a randomized block design.

• An experiment using a matched pairs design.

• An observational study using a simple random sample.

• An observational study using a stratified sample.

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CCSS.HSS.IC.B.3

Toddlers tend to have an abundance of energy. To put that energy to good use a fitness instructor creates a Toddler Fitness class. In this class the participants have to do everything the fitness instructor’s energetic toddler daughter does.

To compare the number of calories burned in Toddler Fitness versus the standard fitness class 40 volunteers are recruited. The volunteers are assigned at random to participate in Toddler Fitness or the standard fitness class. Each participant wears a calorie counting fitness watch. At the end of the class the calories burned by each participant is recorded and the average number of calories burned is calculated for each class.

After the classes ended, the instructor learned that the mean number of calories burned by the participants in Toddler Fitness was significantly greater than the mean number of calories burned by the participants in the standard fitness class.

Which of the following is the most appropriate conclusion?

• There is convincing evidence that Toddler Fitness caused the participants to burn more calories than the standard fitness class, and the conclusion can be generalized to all adults that workout.

• There is convincing evidence that Toddler Fitness caused the participants to burn more calories than the standard fitness class, and the conclusion can be generalized to all students of this fitness instructor.

• There is convincing evidence that Toddler Fitness caused the participants to burn more calories than the standard fitness class, and the conclusion cannot be generalized beyond those in the study.

• Cause-and-effect cannot be established, but there is an association between the type of exercise class taken and the number of calories burned in the population of all adults that workout.

• Cause-and-effect cannot be established, but there is an association between the type of exercise class taken and the number of calories burned in the population of all students of this fitness instructor.

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CCSS.HSS.IC.B.3

In order to estimate the proportion of students that text while driving, a school administrator selects a simple random sample of students from a list of all students at the school who have parking permits. The students are called to the office, one at a time. The administrator asks each student, “Do you text while driving, even though you are not supposed to?” Based on the survey, the administrator estimates that only 2% of students with parking passes text while driving. What potential bias is present in the design of this survey and what is the likely direction of the bias?

• The sample proportion is likely an underestimate of the population proportion due to response bias.

• The sample proportion is likely an underestimate of the population proportion due to undercoverage.

• The sample proportion is likely an underestimate of the population proportion due to nonresponse.

• The sample proportion is likely an overestimate of the population proportion due to response bias.

• The sample proportion is likely an overestimate of the population proportion due to undercoverage.

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CCSS.HSS.IC.B.3