State what the given confidence interval suggests about the two population means

Question

State what the given confidence interval suggests about the two population means. A researcher was interested in comparing the amount of time spent watching television by women and by men. Independent simple samples of 14 women and 17 men were selected, and random each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows. The lowing 99% confidence interval was obtained for mu_1 - mu_2, the difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men: -5.73 hrs

Explanation / Answer

Here 99% confidence interval is given in the question which is

-5.73 Hrs < 1 - 2 < 4.13 Hrs

Here difference interval consisits 0 so which suggests that the two population mean might be equal. There does not appear to be a significant difference between the mean amount of time spent watching tv for women and the mean amount of time spent watching for women. OPtion C is correct.

Here Mean difference in population mean 1 - 2 = x1 -bar - x2-bar = 12.9 - 13.7 = -0.8 Hrs

Pooled standard deviation sp = sqrt [(n1 -1)s12 +(n2 -1)s2 2]/[n1 +n2 -2]

sp = sqrt [(13 * 3.92 + 16 *5.22 )/(13+16) ] = 4.662

standard error of sampling se0 = sp sqrt [1/n1 +1/n2 ] = 4.662 * sqrt [1/14 + 1/17] = 1.6825

critical t value for 99% confidence interval t0.005, 29 = 2.756

99% CI = (x1 -bar - x2-bar) +- t0.005, 29 * SE

= -0.8 + 2.756 * 1.7825

= (-5.73 , 4.13)

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