Question

1. (Hypothetical) The General Social Survey measures the number of hours that individuals spend on the internet each week. Males use the Internet 12.1 hours per week. (standard deviation 10.8; N = 264), while women use the Internet 9.10 hours per week (standard deviation 12.50; N = 300).

a) Test the research hypothesis that men use the internet more hours a than women. Set alpha at .05.

b) Would your decision have been different if alpha were set at .01?

Answer 1

Here we want to test the research hypothesis that men use the internet more hours a than women.

So the null hypothesis ( H₀ ) and the alternative hypothesis ( H_a ) are as follows:

Where = Population mean of time use the Internet per week for men.

= Population mean of time use the Internet per week for women .

Here standard deviations of both the groups are given. So we can use two sample Z test.

Let's use TI-84 Plus calculator.

Step 1: Click on STAT >>>TESTS >>>3: 2-SampZTest...

Step 2: highlight Stats then press enter.

Fill the required information.

Look the following image:

Then click on down arrow

Select > and then enter

THen highlight Calculate and press enter.

So we get the following output:

From the above output, we get .

Z test statistic = 3.0576

p-value = 0.0011

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.0011 which is < 0.05 so we used first rule.

That is we reject null hypothesis

Conclusion: At 5% level of significance there are sufficient evidence to conclude that the  men use the internet more hours a than women.

b) No, because p-value = 0.0011 < 0.01 and so again we can use first decision rule.