Question

A researcher was interested in comparing the amount of time spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was asked how many hours he or she had watched television during the previous week.

The summary statistics are as follows:

Women        Men   _
Sample mean      11.9 hrs      16.9 hrs
Sample SD         4.1 hrs        4.8 hrs
Sample size            14                17


Use this data and a 0.05 significance level to test the claim that the mean amount of time spent watching television by women is smaller than the mean spent watching television by men. Assume that the population variances are equal.

Answer 1

Given:

Women:

n1 = 14, = 11.9, S1 = 4.1

n2 = 17, = 16.9, S2 = 4.8

Hypothesis:

Or mean amount of time spent watching television by women is smaller than the mean spent watching television by men

Test statistic:

t = -3.036

Degrees of Freedom = n1+n2-2 = 14 + 17 - 2 = 29

P-value = 0.0025 ........................Using t table

Conclusion:

P-value < , i.e. 0.0025 < 0.05, That is Reject Ho at 5% level of significance.

Therefore, there is sufficient evidence that the, the mean amount of time spent watching television by women is smaller than the mean spent watching television by men.