statistical techniques 44?

Question

A recent article in the Wall Street Journal reported that the 30-year mortgage rate is now less than 6 percent. A sample of eight small banks in the Midwest revealed the following 30- year rates (in percent):
4.8
5.3
6.5
4.8
6.1
5.8
6.2
5.6


At the .01 significance level, can we conclude that the 30-year mortgage rate for small banks is less than 6 percent? Estimate the p-value.

Answer 1

You can consider the data taken as a random sampling from a population of banks. So you can compute the mean and variance and standard deviation of the data. If the mean is x-bar, and the standard deviation is (sd), then 6 - (x-bar) / (sd/sqrt 7) can be tested as a z-statistic. Without cranking out the numbers, my guess is that you reject the hypothesis at the 0.01 level.

Answer 2

From the data, xbar = 5.5125, s = 0.60578, n = 8

You have to use the t distribution, dof = 7

t value = [5.5125-6] / [0.60578/sqrt(8)]
= -2.276

From t(7) tables the p value is between 0.01 and 0.025.
At the 0;.01 level, there is not enough evidence to conclude the rate is less than 6%.