Question

The serious delinquency rate measures the proportion of homes that are well behind on their mortgage payments. A real estate investor is trying to decide in which of two neighborhoods in Phoenix to buy an investment property. He is trying to decide if the serious delinquency rate differs between the two neighborhoods. He took a sample of 70 homes in neighborhood 1 and found 14 homes were seriously delinquent. He took a sample of 80 homes in neighborhood 2 and 10 homes were seriously delinquent. Specify the null and alternate hypotheses to determine if the delinquency rates in the two neighborhoods are equal and make a conclusion at the 10% significance level. How should the delinquency rate influence the investor’s decision? (Make sure to follow all procedures for hypothesis testing) please show all work

Answer 1

p1cap = X1/N1 = 14/70 = 0.2
p1cap = X2/N2 = 10/80 = 0.125
pcap = (X1 + X2)/(N1 + N2) = (14+10)/(70+80) = 0.16

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 ≠ p2

Rejection Region
This is two tailed test, for α = 0.1
Critical value of z are -1.64 and 1.64.
Hence reject H0 if z < -1.64 or z > 1.64

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.2-0.125)/sqrt(0.16*(1-0.16)*(1/70 + 1/80))
z = 1.25

P-value Approach
P-value = 0.2113
As P-value >= 0.1, fail to reject null hypothesis.

There is no significant difference in the delinquency rate in the two neighborhoods.