Question

A sample of 83 women found that the mean length of time they spent sleeping daily was 7.0 hours with standard deviation 1.8 hours. An independent sample of 65 men found that the mean length of time they spent sleeping daily was 6.6 hours with standard deviation 1.7 hours. At the 5% level of significance, can we show women sleep more on average than men? (a) Do an appropriate test. State conclusions. (b) Find the p-value of the test.

Answer 1

a)

The test hypothesis is

This is a one-sided test because the alternative hypothesis is formulated to detect the difference from the hypothesized mean on the upper side

Now, the value of test static can be found out by following formula:

Degrees of freedom on the t-test statistic are n1 + n2 - 2 = 83 + 65 - 2 = 146

This implies that

Since t0 = 1.3746<1.655357344899022=t{0.05, 146}, we fail to reject the null hypothesis  

We have insufficient evidence to claim that women sleep more on average than men

b)

Using Excel's function =T.DIST.RT(t0,n-1), the P-value for t0 = 1.3746 in an upper-tailed t-test with 146 degrees of freedom can be computed as

Since P = 0.0857 > 0.05, we fail to reject the null hypothesis