A Roper survey reported that 65 out of 500 women ages 1829 s

A Roper survey reported that 65 out of 500 women ages 18-29 said that they had the most say when purchasing a computer; a sample of 700 men ages 18-29 found that 133 men said that they had the most say when purchasing a computer. At , a test will be used to determine if there is a difference between these proportions. What is the null hypothesis?

Solution

Null Hypothesis, There Is No Significance between them Ho: p1 = p2
Alternate Hypothesis, There Is Significance between them H1: p1 != p2
Test Statistic
Sample 1 : X1 =65, n1 =500, P1= X1/n1=0.13
Sample 2 : X2 =133, n2 =700, P2= X2/n2=0.19
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.165
Q^ Value For Proportion= 1-P^=0.835
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.13-0.19)/Sqrt((0.165*0.835(1/500+1/700))
Zo =-2.761
| Zo | =2.761
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =2.761 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != -2.7606 ) = 0.0058
Hence Value of P0.05 > 0.0058,Here we Reject Ho

We cliam that There Is Significance between them