A marketing firm asked a random set of married and single me

A marketing firm asked a random set of married and single men how much they were willing to spend on a vacation. Is there sufficient evidence at ? = 0.05 to conclude that is there a difference in the two amounts?   

Married men

Single men

Sample size

40

50

Sample mean

$920

$845

Population variance

5700

9100

Solution

Ho: mu1=mu2

Ha: mu1 not equal to mu2

The test statistic is

Z=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(920-845)/sqrt(5700/40+9100/50)

=4.16

Given a=0.05, the critical values are Z(0.025)=-1.96 or 1.96 (from standard normal table)

Since Z=4.16 is larger than 1.96, we reject Ho.