The GSS 2010 measures the amount of hours individuals spend on the Internet per week

# The GSS 2010 measures the amount of hours individuals spend on the Internet per week

398.7k points

The GSS 2010 measures the amount of hours individuals spend on the Internet per week. Males use the Internet 10.17 hrs per week (standard deviation = 11.71, N = 118), while women use the Internet 9.08 hours per week (standard deviation = 12.26, N = 157).

a. Test the research hypothesis that men use the Internet more hours than women, set alpha at .05.

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

difference means
test statistic

398.7k points

a) In this case we need to first decide which test statistic to use. Since we are dealing with a difference between two samples are their means, we will use the difference in means test statistic,

$$t = \frac{x_1-x_2}{SE}$$

the standard error in this case can be found using the following,

$$SE = s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$$

where,

$$s_p = \sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}$$

we are given $x_1, x_2, s_1, s_2, n_1$, and $n_2$ so first calculate $s_p$,

$$s_p = \sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}$$

$$= \sqrt{\frac{(118-1)11.71^2+(157-1)12.26^2}{118+157-2}}$$

$$s_p = 12.03$$

so,

$$SE = 12.03 \sqrt{\frac{1}{118}+\frac{1}{157}} \approx 1.47$$

and,

$$t = \frac{10.17-9.08}{1.47} = 0.74$$

the value in the book is 0.757 probably due to rounding errors in the calculation. The associated p-value for this test statistic is approx 0.2 which is greater than the given alpha value. For this reason we fail to reject the null hypothesis. There is no difference in internet use between males and females.

b) because our p-value was 0.2, with alpha at 0.01 we still fail to reject the null hypothesis. Same conclusion.

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