Use the following to answer the question(s) below.
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 0.39%. 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
A) reject the alternative hypothesis.
B) fail to reject the null hypothesis.
C) evidence suggests that there is no significant difference in mean mortgage rates between credit unions and banks.
D) reject the null hypothesis; evidence suggests that there is a significant difference in mean mortgage rates between credit unions and banks.
E) fail to reject the null hypothesis; evidence suggests that the mortgage rates at credit unions are lower than at banks, on average.

Question

Use the following to answer the question(s) below.
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 0.39%. 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
A) reject the alternative hypothesis. 
B) fail to reject the null hypothesis. 
C) evidence suggests that there is no significant difference in mean mortgage rates between credit unions and banks. 
D) reject the null hypothesis; evidence suggests that there is a significant difference in mean mortgage rates between credit unions and banks. 
E) fail to reject the null hypothesis; evidence suggests that the mortgage rates at credit unions are lower than at banks, on average.

Quizplus · Accepted Answer

We need to perform a two-sample t-test with unequal variances, as the sample standard deviations are different. The null hypothesis is that there is no difference in the mean mortgage rates between credit unions and banks, and the alternative hypothesis is that there is a difference.

Using a calculator or software, we get the t-statistic as -6.434 and the p-value as less than 0.0001. As the p-value is less than the significance level of 0.05, we reject the null hypothesis. This means that there is sufficient evidence to conclude that the mean mortgage rates are significantly different between credit unions and banks.

Therefore, the correct answer is D, "reject the null hypothesis; evidence suggests that there is a significant difference in mean mortgage rates between credit unions and banks."

Use the Following to Answer the Question(s) Below