Question

A college graduate is curious about the proportion of graduates who have loan debt 20 years after graduating. Let the proportion of graduates who have loan debt 20 years after graduating be p. If the college graduate wishes to know if the proportion of graduates who have loan debt 20 years after graduating is less than 18%, what are the null and alternative hypotheses?

Answer 1

Answer: Null Hypothesis
`H_(0)`: p = 0.18

Alternative Hypothesis
`H_(a)`: p < 0.18

Explanation: When doing an experiment, first define the hypotheses you want to test. These hypotheses are Null Hypothesis and Alternative Hypothesis

Null Hypothesis is a general assumption and discloses that there is no relationship between the conditions under consideration. It is the hypothesis the researcher is trying to disprove. It is denoted by the symbol
`H_(0)`.

For the college graduate curiosity, the hypothesis the graduate is trying to disprove is that the proportion of students who have loan debt after 20 years of graduation is 18%. Then, Null Hypothesis is
`H_(0)`: p = 0.18

Alternative Hypothesis is the a statement describing a relationship between the collected data. It is what researches try to prove and the results are observations of real causes. It is denoted by the symbol
`H_(a)`.

For the graduate study, the alternative is that the proportion is less tahn 18% or 0.18. Then, Alternative Hypothesis:
`H_(a)`: p < 0.18