38.6k views
5 votes
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).

User Kdon
by
7.2k points

1 Answer

6 votes

Answer:

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

User Stephan Du Toit
by
7.0k points