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Chapter 8: Q.42 (page 497)

Equality for women? Have efforts to promote equality for women gone far enough in the United States? A poll on this issue by the cable network MSNBC contacted 1019adults. A newspaper article about the poll said, 鈥淩esults have a margin of sampling error of plus or minus 3 percentage points.鈥�15

(a) The news article said that 65% of men, but only 43% of women, think that efforts to promote equality have gone far enough. Explain why we do not have enough information to give con铿乨ence intervals for men and women separately.

(b) Would a 95% con铿乨ence interval for women alone have a margin of error less than 0.03, about equal to 0.03, or greater than 0.03? Why? (You see that the news article鈥檚 statement about the margin of error for poll results is a bit misleading.)

Short Answer

Expert verified

From the given information,

a) Without sample sizes for the men and for the women, we can't give confidence intervals for men and women individually.

b) The margin of error for the confidence intervals 0f95%will be greater than0.03

Step by step solution

01

part (a) Step 1: Given Information 

It is given in the question that, confidence intervals = 95%

the margin of error = 0.03

Explain why we do not have enough information to give con铿乨ence intervals for men and women separately.

02

part (a) Step 2: Explanation 

Without sample sizes for the men and for the women, we can't give confidence intervals for men and women individually.

03

part (b) Step 1: Given Information 

It is given in the question that, confidence intervals =

the margin of error =

Would a 95% con铿乨ence interval for women alone have a margin of error less than 0.03, about equal to 0.03, or greater than 0.03? Why?

04

part (b) Step 2: Explanation 

The sample size of women is less than the sample size of both men and women.

Yet the decrease in the size of the sample results in a less accurate prediction therefore an increase in the margin of error. Thus, the margin of error for women will be greater than the3% margin of error for men and women.

Accordingly, the margin of error for the confidence interval of95% will be greater than 0.03.

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Most popular questions from this chapter

Many teens have posted profiles on sites such as Facebook and My Space. A sample survey asked random samples of teens with online profiles if they included false information in their profiles. Of 170younger teens (ages 12to 14) polled, 117said 鈥淵es.鈥� Of 317older teens (ages 15to 17) polled, 152 said 鈥淵es.鈥�6 A 95% confidence interval for the difference in the population proportions (younger teens 鈥� older teens) is 0.120 to 0.297. Interpret the confidence interval and the confidence level

You have measured the systolic blood pressure of an SRS of 25company employees. A 95%confidence interval for the mean systolic blood pressure for the employees of this company is (122,138). Which of the following statements gives a valid interpretation of this interval?

(a) 95%of the sample employees have systolic blood pressure between 122and138.

(b) 95%of the population of employees have systolic blood pressure between 122and138.

(c) If the procedure were repeated many times, 95%of the resulting confidence intervals would contain the population mean systolic blood pressure.

(d) The probability that the population mean blood pressure is between 122and138is 0.95.

(e) If the procedure were repeated many times, 95%of the sample means would be between122and138.

You have an SRS of 23 observations from a Normally distributed population. What critical value would you use to obtain a 98% confidence interval for the mean M of the population if S is unknown?

(a) 2.508

(b) 2.500

(c) 2.326

(d) 2.183

(e) 2.177

Conditions Martin says that the relative importance of the three conditions for performing inference is, in order from most to least important, Independent, Normal, and Random. Write a brief note to Martin explaining why he is incorrect.

Abstain from drinking In a Harvard School of Public Health survey, 2105 of 10,904 randomly selected U.S. college students were classified as abstainers (nondrinkers).

(a) Construct and interpret a 99% confidence interval forp. Follow the four-step process.

(b) A newspaper article claims that 25% of U.S. college students are nondrinkers. Use your result from (a) to comment on this claim.
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