A researcher was interested in comparing the amount of time spent watching telev

Question

A researcher was interested in comparing the amount of time spent watching television by women and by men independent simple random sample of women and 17 men were selected from normally distributed populations, and each person was asked how many hours he or she had watched television during the previous week. summary statistics are as follows. DO not assume that the populate standard deviations are equal. With alpha = .10, test the claim that the mean time spent watching television by women is less than that of men. Identify the null hypothesis, alternative hypothesis, test statistic and/or P-value, critical value(s), and conclusion that addresses the original claim.

Explanation / Answer

Here population standard deviation or population are not equal.

Null Hypothesis : H0 : Tv hours for women are not less than Tv hours for men in one week (Women >= man)

ALternative Hypothesis : Ha : Tv hours are same for men and women in one week (Women <man)

Test Statistic : when two standard deviations are not equal

t = (xmen - xwomen) / sqrt (s12/n1 + s22/n2) = ( 14.0 - 12.6)/ sqrt (3.9*3.9/14 + 5.2*5.2/17) = 1.4/1.6361 = 0.8557

for alpha = 0.10 and

dF = (s12/n1 + s22/n2)2 / [ (1/n1 - 1)(s12/n1)2 + (1/n2 - 1)(s22/n2)2]

= 7.1664/ [ (0.0908 + 0.1581)] = 28.79 = 29

for alpha = 0.1, dF = 29

tcritical = 1.311

and t < tcritical ; so we cannot reject the null hypothesis and we can conclude that there is no difference between men and women tv hours.

P- value = 0.1995; The result is not significant at p < 0.10.

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