Question

A random sample of 400 morning shoppers showed that 130 were men. A random sample of 480 evening shoppers showed 187 to be men. Use a 5% level of significance to test for a significant difference in the proportion of morning and evening male shoppers. What is your conclusion?

Answer 1

n1= 400
x1 = 130
n2 = 480
x1 = 187

phat1 = x1/n1 = 130/400 = .325

phat2 = x2/n2 = 187/480 = .3896

pbar = (x1 + x2)/(n1+n2) = (130 +187)/(400+480) = .36
qbar = 1- pbar = .64

z = (325- .3896)/sqrt(.36*.64/400+ .36*.64/480)

z = -1.99
If p-value greater than alpha
Fail to reject Ho
If p-value less than alpha
Reject Ho

p-value = 0.047