Question 834:

Asked on December 9, 2009

Tags: Hypothesis Test , 2-sample t-test

1

Answer:

No answer provided yet.For this test we need to determine whether the difference in means represents a real difference in population means or is just an artifact of sampling error.  We will conduct a 2-sample t-test on the mean.

1. The Null Hypothesis is that there is no difference in the political participation between men and women. The alternative Hypothesis is that men have greater political participation.
2. We will conduct a 2-sample t-test and reject the Null Hypothesis is the p-value is less than the alpha value of .05.
3. The test-statistic t* is found as:
1. Find the difference between the sample means = 1.48-1.44 = .04
2. Divide the difference between the sample means and the standard error of the difference. The standard error of the difference is found as the pooled standard deviation which results in .00911
3. The test statistic t* is then .04/.009 = 4.386.
4. We want the 1-sided area (since our alternative hypothesis is that men participate more) from the t-distribution on n1+n2-2 degrees of freedom = 705. The p-value is less than .0001.
4. Since the p-value is well less than the alpha of .05 we reject the Null Hypothesis.
5. We conclude that there is sufficient evidence that men have greater levels of political participation than women.