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)

Answer 1

The null hypothesis (H0) for the test is that the proportions are the same.

The alternate hypothesis (H1) is that the proportions are not the same.

p1 = proportion in neighborhood 1 = 14/70 = 0.2; n1: no. of samples for neighborhood 1 = 70

p2 = proportion in neighborhood 2 = 10/80 = 0.125; n2: no. of samples for neighborhood 2 = 80

pooled proportion, p = (14+10) / (80+70) = 0.16

Test Statistic,

=1.25

The critical value of Z corresponding to 10% significance level, Zcrit = 1.645 (for a 2-tailed test)

Since Ztest < Zcrit, we conclude that there is not enough evidence to reject the Null Hypothesis.

So the difference in the delinquency rates between the two neighborhoods is not significant.

The investor can choose either of the two localities for investment.