Question

In a survey taken in 2013, 20 out of 30 women and 17 out of 35 men said they felt much better about the state of our economy today than they did a few years ago. Do these data provide sufficient evidence at the 0.01 level of significance to conclude that women are more likely than men to feel better about the economy today than they did a few years ago? Use the P-Value Method of Testing. In your work space below, you will need to have - 1. The null hypothesis, Ho (4 points) 2. The alternative hypothesis, H1 (4 points) 3. The test statistic (8 points) 4. The type of test(left, right, two-tailed) and the p-value (5 points) 5. The decision to accept Ho or reject Ho (4 points)

Answer 1

Given : For women: n1=30 x1=20

For male : n2=35 x2=17

Significance level=0.01

The sample proportions are given by ,

p1=x1/n1=20/30=0.6667

p2=x2/n2=17/35=0.4857

The pooled estimate is ,

Q=1-P=0.4308

1. The null hypothesis is ,

2. The alternative hypothesis is ,

3. The test statistic under Ho is ,

4. The test is right tailed test

P value =

5. Decision : Here , P value = 0.0708 >

Therefore , fail to reject Ho at significance level

Conclusion : Hence , there is not sufficient evidence to conclude that the women are more likely than men to feel better about the economy today than they did a few years ago.