A sample of 30 year fixed mortgage rates at 12 randomly chosen credit unions yields a mean rate of 6.65 % and a sample standard deviation of 0.38%. A sample of 30 year
Fixed mortgage rates at 16 randomly selected banks yields a mean rate of 7.05% and a
Sample standard deviation of 0.22%. Are the mean rates different between credit unions
And banks? Relevant output is shown below. Which of the following is true? $\begin{array} { l r r r r } \text { Sample } & \mathbb { N } & \text { Mean } & \text { StDev } & \text { SE Mean } \ 1 & 12 & 6.650 & 0.390 & 0.11 \ 2 & 16 & 7.050 & 0.220 & 0.055 \end{array}$
Difference $= m u ( 1 ) = m u$ (2)
Bstimate for difference: $\quad - 0.400$
95 옿 CI for difference: $( - 0.666 , - 0.134 )$
T-Test of difference $= 0$ (vs not $= ) :$ T-Value $= - 3.19$ P-Value $= 0.006 \quad$ DF $= 16$
A) This is a paired design.
B) This is a test of two means from independent samples.
C) This is a one tailed test.
D) Both A and C.

Question

Quizplus · Accepted Answer

The given scenario involves comparing the mean rates of two independent samples, one from credit unions and the other from banks. Therefore, it is a test of two means from independent samples. The fact that the samples have different sizes and standard deviations indicates that a t-test is appropriate. Additionally, the 95% confidence interval does not contain 0, and the p-value is less than 0.05, which suggests strong evidence of a significant difference between the mean mortgage rates of credit unions and banks. Therefore, it is a two-tailed test. The scenario is not a paired design as each credit union and bank has its independent interest rate, which is not dependent on any other credit union or bank.

A Sample of 30 Year Fixed Mortgage Rates at 12