Question

An economist believes that interest rates for thirty-year fixed-rate mortgage loans are decreasing. To investigate this further, the economist would like to test the claim that the percent of thirty-year fixed-rate mortgage loans that have a 4.75 percent interest rate is less than 22%. They decide to complete a hypothesis test at a 1% significance level. They sample 40 thirty-year fixed-rate mortgage loans, and determine the sample percent to be 12.5%. The following is the data from this study:

Sample size = 40 thirty year fixed-rate mortgage loans
Sample proportion = 0.125
Identify the roll and alternative hypothesis for this study by nilling in the blanks with the correct (=, <, or > or to represent the correct hypothesis).

Answer 1

The null hypothesis is
`H_0: p = 0.22`

The alternate hypothesis is
`H_1: p < 0.22`

Explanation:

To investigate this further, the economist would like to test the claim that the percent of thirty-year fixed-rate mortgage loans that have a 4.75 percent interest rate is less than 22%.

At the null hypothesis, we test that the proportion is of 22%, that is:

`H_0: p = 0.22`

At the alternate hypothesis, we test that the proportion is less than 22%, that is:

`H_1: p < 0.22`