Question

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. At the 0.05 level of significance, the correct conclusion is



I. Do not reject the null hypothesis.
II. Reject the null hypothesis.
III. Evidence suggests that there is a significant difference in mean mortgage rates between credit unions and banks.

I only

II only

III only

Both I and III

Both II and III

Answer 1

Solution: Here using the thses given summarised data we solve this problem using the mintab statistical software as below and mintab output will be

hypothesis

H0: There mo mean rates different between credit unions and banks

vs

H1:

There is mean rates different between credit unions and banks

i.e.

H0:  μ (1) - μ (2) = 0

vs

H1:  μ (1) - μ (2) 0

Difference = μ (1) - μ (2)
Estimate for difference: -0.4000
95% CI for difference: (-0.5605, -0.2395)
T-Test of difference = 0 (vs ≠): T-Value = -4.99 P-Value = 0.000 DF = 58
Both use Pooled StDev = 0.3105

Now using the p-vlaue we say that the we reject H0 at 0.05 level of significance becasue p-value is less than the 0.05

now given that

I. Do not reject the null hypothesis.
II. Reject the null hypothesis.
III. Evidence suggests that there is a significant difference in mean mortgage rates between credit unions and banks.

therefore answer will be

Answer : Both II and III

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