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Chapter 12: Q. 58 (page 819)

About 1100high school teachers attended a weeklong summer institute for teaching AP Statistics classes. After learning of the survey described in Exercise 56, the teachers in the AP Statistics class wondered whether the results of the tattoo survey would be similar for teachers. They designed a survey to find out. The class opted to take a random sample of 100teachers at the institute. One of the first decisions the class had to make was what kind of sampling method to use.

a. They knew that a simple random sample was the “preferred” method. With 1100teachers in 40different sessions, the class decided not to use an SRS. Give at least two reasons why you think they made this decision.

b. The AP Statistics class believed that there might be systematic differences in the proportions of teachers who had tattoos based on the subject areas that they taught. What sampling method would you recommend to account for this possibility? Explain a statistical advantage of this method over an SRS.

Short Answer

Expert verified

(a) Teachers are split up into forty distinct sessions, finding each one would take a long time and effort.

If cluster sampling were used with each distinct session as a cluster, all teachers from a handful of these clusters would be included in the sample.

(b) It is advisable to employ stratified random sampling after include teachers from each subject area in the sample.

Step by step solution

01

Part (a) Step 1: Given information

About 1100high school teachers attended a weeklong summer institute for teaching AP Statistics classes.

The class opted to take a random sample of 100teachers at the institute.

02

Explanation

Because the 1100 teachers are split up into forty distinct sessions, finding each one would take a long time and effort.

If cluster sampling were used with each distinct session as a cluster, all teachers from a handful of these clusters would be included in the sample. This method of sampling would be far more convenient than a basic random sample.

03

Part (b) Step 1: Given information

About 1100high school teachers attended a weeklong summer institute for teaching AP Statistics classes.

The class opted to take a random sample of 100teachers at the institute.

04

Part (b) Step 2: Explanation

It is advisable to employ stratified random sampling after including teachers from each subject area in the sample.

In this situation, stratified random sampling draws a simple random sample from separate subgroups, which would be every topic area.

This allows us to compare the topic area to the number of tattooed teachers.

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Most popular questions from this chapter

Could mud wrestling be the cause of a rash contracted by University of Washington students? Two physicians at the university’s student health center wondered about this when one male and six female students complained of rashes after participating in a mud-wrestling event. Questionnaires were sent to a random sample of students who participated in the event. The results, by gender, are summarized in the following table.

Here is some computer output for the preceding table. The output includes the observed counts, the expected counts, and the chi-square statistic.

From the chi-square test performed in this study, we may conclude that

a. there is convincing evidence of an association between the gender of an individual participating in the event and the development of a rash.

b. mud wrestling causes a rash, especially for women.

c. there is absolutely no evidence of any relationship between the gender of an individual participating in the event and the subsequent development of a rash.

d. development of a rash is a real possibility if you participate in mud wrestling, especially if you do so regularly.

e. the gender of the individual participating in the event and the development of a rash are independent.

Multiple Choice Select the best answer for Exercises 23-28. Exercises 23-28 refer to the following setting. To see if students with longer feet tend to be taller, a random sample of 25students was selected from a large high school. For each student, x=footlength&y=heightwere recorded. We checked that the conditions for inference about the slope of the population regression line are met. Here is a portion of the computer output from a least-squares regression analysis using these data:

Which of the following would have resulted in a violation of the conditions for inference?

a. If the entire sample was selected from one classroom

b. If the sample size was 15instead of 25

c. If the scatterplot of x=footlength&y=heightdid not show a perfect linear relationship

d. If the histogram of heights had an outlier

e. If the standard deviation of foot length was different from the standard deviation of height

Braking distance, again How is the braking distance for a car related to the amount of tread left on the tires? Here are the braking distances (measured in car lengths) for a car making a panic stop in standing water, along with the tread depth of the tires (in 1/32inch):

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a. Below is a scatterplot of the natural logarithm of the number of surviving bacteria versus time. Based on this graph, explain why it would be reasonable to use an exponential model to describe the relationship between the count of bacteria and the time.


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Could mud wrestling be the cause of a rash contracted by University of Washington students? Two physicians at the university’s student health center wondered about this when one male and six female students complained of rashes after participating in a mud-wrestling event. Questionnaires were sent to a random sample of students who participated in the event. The results, by gender, are summarized in the following table.

Here is some computer output for the preceding table. The output includes the observed counts, the expected counts, and the chi-square statistic.

The cell that contributes most to the chi-square statistic is

a. men who developed a rash.

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c. women who developed a rash.

d. women who did not develop a rash.

e. both (a) and (d).
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