Chapter 9.1, Problem 9.5E

a)

To determine

To find the parameter p.

Answer to Problem 9.5E

Population proportion is the proportion of women in the U.S. who think they do not get enough time for themselves.

Explanation of Solution

Given:

A New York Times Poll on women's issues interviewed 1025 women randomly selected from the United States, excluding Alaska and Hawaii. Of the women in the sample, 482 said they do not get enough time for themselves. Although the samples in national polls are not SRSs, they are close enough that our method gives approximately correct confidence intervals

In above study, let us assume that,

  $x$ =Number of women said they do not get enough time for themselves = 482

n = Total number of selected women = 1025

Here, population proportion is the proportion of women in the U.S. who think they do not get enough time for themselves.

b)

To determine

To find the95% confidence interval for p

Answer to Problem 9.5E

The 95% confidence interval is, (0.4390,0.5014)

Explanation of Solution

Given:

  $x$ =Number of women said they do not get enough time for themselves = 482

n = Total number of selected women = 1025

Formula:

Sample proportion:

  $\widehat{p}=\frac{x}{n}$

Confidence interval for population proportion is,

  $CI=\widehat{p}\mp Zc\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}$

Calculation:

Sample proportion,

  $\widehat{p}=\frac{482}{1025}=0.4702$

Now need to find Zc

The level of significance is = a=0.05

Therefore, Zc = Z _a/2 = 1.96 ..Using standard normal table

Therefore, the 95% confidence interval for population proportion is,

  $\begin{array}{l}\left(0.4702-1.96\sqrt{\frac{0.4702(1-0.4702)}{1025}},0.4702+1.96\sqrt{\frac{0.4702(1-0.4702)}{1025}}\right)\\ \left(0.4390,0.5014\right)\end{array}$

c)

To determine

To explain the 95% confidence interval for p

Explanation of Solution

Given:

The 95% confidence interval is, (0.4390,0.5014)

We are 95% confidence that the proportion of women in the U.S. who think that they do not get enough time for themselves is between 0.4390 and 0.5014