Q.42 - The Practice of Statistics for AP

Question

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 $1019$ adults. A newspaper article about the poll said, “Results have a margin of sampling error of plus or minus 3 percentage points.”$15$ 

(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 confidence intervals for men and women separately.

(b)  Would a $95$% confidence 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’s statement about the margin of error for poll results is a bit misleading.) 

Step-by-Step Solution

Answer

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 0f $95\%$ will be greater than $0.03$

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 confidence intervals for men and women separately. 

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. 

part (b) Step 1: Given Information

It is given in the question that, confidence intervals =

the margin of error =

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

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 the $3$% margin of error for men and women.

Accordingly, the margin of error for the confidence interval of$95$% will be greater than $0.03$.