Question

In an early 2020 sample of 700 Chattanooga residents, 90 indicated that they had refinanced their home mortgages in 2019. A sample of 600 residents of Atlanta taken during the same time frame indicated that 44 had refinanced in 2019. At the 5% significance level, test to see if there a difference between the proportions of residents in the two cities who refinanced in 2019. Use the provided text field to show the following 5-Step hypothesis testing process details.

Ho :

Ha :

α =

Test Statistic:

Rejection decision and reasoning:

Conclusion (Interpret your rejection decision in the context of the problem):

Answer 1

Ans:

alpha=0.05

sample proportion 1=90/700=0.1286

sample proportion 2= 44/600=0.0733

pooled proportion=(90+44)/(700+600)=0.1031

Test statistic:

z=(0.1286-0.0733)/SQRT(0.1031*(1-0.1031)*((1/700)+(1/600)))

z=3.27

p-value=2*P(z>3.27)=0.0010

As,p-value<0.05,we reject the null hypothesis.

Conclusion:

There is sufficient evidence to conclude that there is a difference between the proportions of residents in the two cities who refinanced in 2019