Question

a recent study in compare the time spent together by a single and dual earner couples was 61 minutes per day, with a standard deviation of 15.5 minutes. for the Dual earner couples the mean number of minutes spent watching television was 48.4 minutes and a standard deviation of 18.1 minutes. at the 0.01 significant level we can conclude that the single earner couples on the average spend more time watching television together? there are 15 single earned and 12 dual earner couples studied. for calculation assume the single earner as the first sample

Answer 1

H₀:

H₁:

The test statistic t = ()/sqrt(s1^2/n1 + s2^2/n2)

                             = (61 - 48.4)/sqrt((15.5)^2/15 + (18.1)^2/12)

                             = 1.91

DF = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

      = ((15.5)^2/15 + (18.1)^2/12)^2/(((15.5)^2/15)^2/14 + ((18.1)^2/12)^2/11)

      = 22

At alpha = 0.01, the critical value is t^* = 2.508

Since the test statistic value not greater than critical value (1.91 < 2.508), so we should not reject the null hypothesis.

So at 0.01 significance level, we cannot conclude that the single earner couples on the average spend more time watching television together.