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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 鈥減referred鈥� 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

Can physical activity in youth lead to mental sharpness in old age? A 2010study investigating this question involved9344randomly selected, mostly white women over age 65from four U.S. states. These women were asked about their levels of physical activity during their teenage years, 30s,50 s, and later years. Those who reported being physically active as teens enjoyed the lowest level of cognitive decline-only 8.5% had cognitive impairment-compared with 16.7% of women who reported not being physically active at that time.
(a) State an appropriate pair of hypotheses that the researchers could use to test whether the proportion of women who suffered a cognitive decline was significantly smaller for women who were physically active in their youth than for women who were not physically active at that time. Be sure to define any parameters you use.
(b) Assuming the conditions for performing inference are met, what inference method would you use to test the hypotheses you identified in part (a)? Do not carry out the test.
(c) Suppose the test in part (b) shows that the proportion of women who suffered a cognitive decline was significantly smaller for women who were physically active in their youth than for women who were not physically active at that time. Can we generalize the results of this study to all women aged65 and older? Justify your answer.
(d) We cannot conclude that being physically active as a teen causes a lower level of cognitive decline for women over 65, due to possible confounding with other variables. Explain the concept of confounding and give an example of a potential confounding variable in this study.

A study of road rage asked random samples of 596men and 523women about their behavior while driving. Based on their answers, each respondent was assigned a road rage score on a scale of 0-20. The respondents were chosen by random-digit dialing of telephone numbers. Are the conditions for inference about a difference in means satisfied?

a. Maybe; the data came from independent random samples, but we should examine the data to check for Normality.

b. No; road rage scores on a scale of 0-20can鈥檛 be Normal.

c. No; a paired t-test should be used in this case.

d. Yes; the large sample sizes guarantee that the corresponding population distributions will be Normal.

e. Yes; we have two independent random samples and large sample sizes, and the10% condition is met.

A researcher from the University of California, San Diego, collected data on average per capita wine consumption and heart disease death rate in a random sample of 19 countries for which data were available. The following table displays the data

Is there convincing evidence of a negative linear relationship between wine consumption and heart disease deaths in the population of countries?

Could mud wrestling be the cause of a rash contracted by University of Washington students? Two physicians at the university鈥檚 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.

Which sampling method was used in each of the following settings, in order from I to IV?

I. A student chooses to survey the first 20 students to arrive at school.

II. The name of each student in a school is written on a card, the cards are well mixed, and 10 names are drawn.

III. A state agency randomly selects 50 people from each of the state鈥檚 senatorial districts.

IV. A city council randomly selects eight city blocks and then surveys all the voting-age residents on those blocks.

a. Voluntary response, SRS, stratified, cluster

b. Convenience, SRS, stratified, cluster

c. Convenience, cluster, SRS, stratified

d. Convenience, SRS, cluster, stratified

e. Cluster, SRS, stratified, convenience
See all solutions

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