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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

To assess the accuracy of a laboratory scale, a standard weight known to weigh 10grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is 10grams if the scale has no bias). In previous studies, the standard deviation of the scale readings has been about 0.0002gram. How many measurements must be averaged to get a margin of error of 0.0001with 98% confidence? Show your work.

Auto emissions Refer to Exercise 6. Below your sketch, choose one value of x inside the shaded region and draw its corresponding confidence interval. Do the same for one value of x outside the shaded region. What is the most important difference between these intervals? (Use Figure 8.5, on page 474, as a model for your drawing.)

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(a) Explain what the margin of error means to someone who knows little statistics.

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Can you taste PTC? PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 75% of Italians can taste PTC, for example. You want to estimate the proportion of Americans who have at least one Italian grandparent and who can taste PTC.

(a) How large a sample must you test to estimate the proportion of PTC tasters within 0.04with 90% con铿乨ence? Answer this question using the 75% estimate as to the guessed value for p鈭�.

(b) Answer the question in part (a) again, but this time use the conservative guess p鈭�=0.5. By how much do the two sample sizes differ?

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