Question

The U.S. Census Bureau publishes information on the ages of married couples. Suppose we want to determine whether, in thew U.S., the mean age of married men differs from the mean age of their wives. A random sample of married couples is taken and their ages are recorded. Perform a hypothesis test at the 0.05 level of significance to determine if the mean age of husbands differs from the mean age of their wives.

Husband	24	33	45	72	31	42	57	29	27
Wife	20	31	44	23	27	39	56	29	24
Difference

Answer 1

Husband	24	33	45	72	31	42	57	29	27
Wife	20	31	44	23	27	39	56	29	24
Difference	4	2	1	49	4	3	1	0	3

difference, d = husband age - wife age

H0: mu(d) = 0
Ha: mu(d) not equal 0

xbar = 7.44
s = 15.6454
n = 9

test statistic,
t = (xbar - 0)/(s/sqrt(n))
t = (7.44 - 0)/(15.6454/sqrt(9))
t = 1.43

p-value = 0.1906
As p-value > 0.05, fail to reject H0
There are not significant evidence to conclude that the mean age of husbands differs from the mean age of their wives.