Download A recent study compared the time spent together by

A recent study compared the time spent together by single and dual earner couples.
According to the records kept by the wives during the study, the mean amount of
time spent together watching television among the single earner couples was 61
minutes per day, with a standard deviation of 15.5 minutes. For the dual earner
couplers, the mean number of minutes spent watching television was 48.4 minutes,
with a standard deviation of 18.1 minutes. At the .01 significance level, can we
conclude that the single earner couples on average spend more time watching
television together? There were 15 single earner and 12 dual earner couples studied.
Note: Use the five-step hypothesis testing procedure to solve the following exercises.
Solution:
Let “X1” represent the time spent together by single earner couples.
Let “X2” represent the time spent together by dual earner couples.
x 1 = 61
s1 = 15.5
n1 = 15
x2 = 48.4
s2 = 18.1
n2 = 12
Ho: There is no difference in the mean time of watching between single and dual
earner couples.
Ha: The single earner couples on average spend more time watching television
together
Test statistic:
t = (x1 - x2 ) / S  (1/n1+1/n2)
S = [ ( n1-1)s1² + (n2-1)s2² ] / [ n1+n2-2]
S =  (3363.5+ 3603.71) / 25
S = 16.69
t
= ( 61 – 48.4 ) / 16.69  (1/15+1/12)
t =12.6 / 6.464
t = 1.949
The table value at 25 df at 0.01 level is 2.4851
Since the calculated value is less than the table value, we accept Ho.
There is no difference in the mean time of watching between single and dual earner
couples.