In order to estimate the mean 30-year fixed mortgage rate for a home loan in the united states, a random sample of 28 recent loans is taken. the average calculated from this sample is 5.25%. it can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.50%. compute 90% and 99% confidence intervals for the population mean 30-year fixed mortgage rate.

a) (0.0509, 0.0541)

b) (0.05224, 0.05276)

Step-by-step explanation:

Formula to find the confidence interval for population mean :-

We assumed that 30-year fixed mortgage rates are normally distributed .

Given : Sample size : , which is less than  30 so it is a small sample , so we apply t-test.

Sample mean :

Standard deviation :

a) Significance level :

Critical value :

Now, the 90% confidence intervals for the population mean 30-year fixed mortgage rate will be:-

b) Significance level :

Critical value :

Now, the 99% confidence intervals for the population mean 30-year fixed mortgage rate will be:-

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

tangent

step-by-step explanation: