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Chapter 12: Q. 56 (page 818)

Tattoos: What per cent of U.S. adults have one or more tattoos? The Harris Poll conducted an online survey of 2302adults and found 29% of respondents had at least 1 tattoo. According to the published report, 鈥淩espondents for this survey were selected from among those who have agreed to participate in Harris Interactive surveys.鈥� Explain why it would not be appropriate to use these data to construct a 95% confidence interval for the proportion of all U.S. adults who have tattoos.

Short Answer

Expert verified

The random condition was not met.

Step by step solution

01

Given information

Online survey of 2302 adults and found 29% of respondents had at least 1 tattoo.

02

Explanation

Independent, Random, and Normal are the three requirements for calculating the95% confidence interval for the proportion.

The sample was acquired using a voluntary response sample, which is not representative of the entire population, hence the random condition was not met.

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Most popular questions from this chapter

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.

The following back-to-back stem plots compare the ages of players from two minor-league hockey teams (1/7=17 years)

Which of the following cannot be justified from the plots?

a. Team A has the same number of players in their 30sas does Team B.

b. The median age of both teams is the same.

c. Both age distributions are skewed to the right.

d. The range of age is greater for Team A

e. There are no outliers by the1.5IQR rule in either distribution.

Which of the following statements about the t distribution with degrees of freedom dfis (are) true?

I. It is symmetric.

II. It has more variability than the t distribution with df+1degrees of freedom. III. III. As df increases, the t distribution approaches the standard Normal distribution.

a. I only

b. II only

c. III only

d. I and III

e. I, II, and III

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.

Recycle and Review Exercises 29-31 refer to the following setting. Does the color in which words are printed affect your ability to read them? Do the words themselves affect your ability to name the color in which they are printed? Mr. Starnes designed a study to investigate these questions using the 16 students in his AP Statistics class as subjects. Each student performed the following two tasks in random order while a partner timed his or her performance: (1) Read 32words aloud as quickly as possible, and (2) say the color in which each of 32words is printed as quickly as possible. Try both tasks for yourself using the word list given.

Color words (10.3) Now let's analyze the data,

a Calculate the difference (Colors-Words) (Colors - Words) for each subject and surmmarize thedistribution of differences with a boxplot. does the graph provide evidence of a difference in the average time required to perform the two tests? Explain your answer.

b. Explain why it is not safe to use paired & procedures to do inference about the mean difference in time in complete the Two tasks.
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