# Question #fd2d3

Jul 15, 2015

a) H0: M = 32 Vs Ha:M >32

#### Explanation:

It is usually best to STATE the hypothesis in verbal form before trying to write it out as an equation. This avoids confusion and helps in constructing the mathematical relationship. The most important thing about a null hypothesis for testing is that is MUST be binary - only ONE of TWO choices is possible. Generally, you make your null hypothesis the thing that you really want disprove Then, your alternative hypothesis is just the opposite.

In the first example, the null hypothesis would be:
"The median is less than 32." If this is proved FALSE by the statistical analysis, then you already have your answer of "at least, or greater than 32". If it is TRUE, then you have shown that it cannot be 32, or any higher.

Once you have this statement, the correct set-up of your equation and interpretation of the numerical statistical test results will be much easier. The originally posted equation answer does NOT provide a correct answer, because it is testing only for the actual value of 32, and the implication of being on one side or the other is not included logically. It also does not represent a true binary choice. A correct formulation would be:

H0: M<32 ; H1: M>=32