Do women really spend less money on Valentines Day as compar

Do women really spend less money on Valentines Day as compared to men? A recent survey found that men spend an average of $39.50 while women spend an average of $25.00. Assume that these data were based on a sample of 100 men and 100 women and the population standard deviations of spending for men and women are $32 and $25, respectively. Let u1 = Women Let u2 = Men

Solution

Set Up Hypothesis
Null, women really spend less money on Valentines Day as compared to men Ho: u1 < u2
Alternate, not Ho H1: u1 > u2
Test Statistic
X(Mean)=39.5
Standard Deviation(s.d1)=32
Number(n1)=100
Y(Mean)=25
Standard Deviation(s.d2)=25
Number(n2)=100
we use Test Statistic (Z) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
Zo=39.5-25/Sqrt((1024/100)+(625/100))
Zo =3.57
| Zo | =3.57
Critical Value
The Value of |Z | at LOS 0.1% is 1.282
We got |Zo | =3.571 & | Z | =1.282
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail -Ha : ( P > 3.57 ) = 0.00018
Hence Value of P0.1 > 0.00018,Here we Reject Ho

We don\'t have evidence that women really spend less money on Valentines Day as compared to men