Question

In a survey of 1,000 women aged 22 to 35 who work full time, 545 indicated that they would be willing to give up some personal time in order to make more money. The sample was selected in a way that was designed to produce a sample that was representative of women in the targeted age group.

a. Do the sample data provide convincing evidence that the majority of women age 22 to 35 who work full-time would be willing to give up some personal time for more money? Test the relevant hypotheses using α = .01.
b. Would it be reasonable to generalize the conclusion from Part (a) to all working women? Explain why or why not.

Answer 1

Yes, there is convincing evidence that the majority of women age 22 to 35 who work full-time would be willing to give up some personal time for more money.

No ;

Explanation:

n = 1000

x = 545

Phat = x / n = 545/1000 = 0.545

H0: p ≤ 0.5

H1: μ > 0.5

The test statistic :

(phat - p0) ÷ √(p(1 - P0) / n)

Test statistic :

(0.545 - 0.5) ÷ √(0.5(0.5) / 1000)

0.045 / 0.0158113

Test statistic = 2.846

α = 0.01

Decison :

Reject H0 ; if Pvalue < α

Using the Pvalue from Test statistic (Z) calculator :

Pvalue = 0.002214

With Pvalue < α ; We reject H0 and conclude that there is convincing evidence that the majority of women age 22 to 35 who work full-time would be willing to give up some personal time for more money.

No, making generalization about all women would not be reasonable as the data employed for the research mainly focuses on a particular