Below are the summary statistics from a researcher who compared the amount of ti

Question

Below are the summary statistics from a researcher who compared the amount of time spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected from normally distributed populations, and they were asked to report how many hours of TV were watched during the previous week. Do not assume that the population standard deviations are equal. Use a 0.05 significance level to test the claim that the mean time spent watching television by women is less than the mean time spent watching television by 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

Hypothesis:

Ho : x1 - x2 > = 0

Ha; x1 - x2 < 0

Test statistic:

SE = sqrt [(s12/n1) + (s22/n2)]

SE = sqrt [(42/15) + (5.12/18]

= 2.51

t = [ (x1 - x2) - d ] / SE

= [ (12.8 - 14) - 0 ] / 2.51 = - 0.48

Now, we need to find p value by using t = -0.48 , df = 15 + 18 - 2 = 31

p value = .3172

Critical value for 0.05 for left tailed test = -1.69

Here, P value is greater than 0.05 so we fail to reject the null hypothesis.

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