Random samples of 5 Japanese women and 10 Japanese men showe

Random samples of 5 Japanese women and 10 Japanese men showed an average life span of 83 years for the women and 77 years for the men. The standard deviation was 2 years for the women and 1 year for the men. Calculate a 95% confidence interval for the difference in average life spans (women men). Assume that the life spans are normally distributed, but do not assume the population variances are equal, and use the conservative “by-hand” estimate for the degrees of freedom.

Answer: (3.36, 8.64)

I\'m not sure how to get to the answer given.

Solution

The data given can be tabulated as follows:

The mean of Group One minus Group Two equals 6.00

Std error for difference = 0.760

Df = 13

Margin of error = std error x t alpha/2

= 2.64

Hence confidence interval = (3.36, 8.64)