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).