The mortgage department of a large bank is interested in the nature of loans of first-time borrowers. This information will be u
sed to tailor their marketing strategy. They believe that 40% of first-time borrowers take out smaller loans than other borrowers. They perform a hypothesis test to determine if the percentage is the same or different from 40%. They sample 100 first-time borrowers and find 53 of these loans are smaller than the other borrowers. For the hypothesis test, they choose a 5% level of significance. What would be the null and alternative hypotheses
The null hypothesis is the statement or claim that is believed or assumed to be true. In this case, the null hypothesis is "They believe that 40% of first-time borrowers take out smaller loans than other borrowers". Since we are dealing with proportion, we will denote it with p. The null hypothesis would be
p = 0.4
The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected. The alternative hypothesis is "They perform a hypothesis test to determine if the percentage is the same or different from 40%". It would be written as
For the function f(x) = 4^(x-1) +2 the average rate of change on the interval [1, 2] is found by computing (f(2) - f(1))/(2 - 1) = ((4^1+2) - (4^0+2)/1 = (6-3) = 3
