Question

What is the correct methodology for defining null and alternative hypothesis? Give an example

Answer 1

Below are examples for a one-sample test. For more than one sample, the hypotheses are set up a bit differently but the fundamentals are the same.

Options for the null (one-sample):

Ho: µ = ? -->meaning: population mean is equal to some value.
Or...
Ho: µ ≤ ? -->meaning: population mean is less than or equal to some value.
Or...
Ho: µ ≥ ? -->meaning: population mean is greater than or equal to some value.

The null hypothesis ALWAYS uses an equals sign.

Options for the alternative (one-sample):

Ha: µ < ? -->meaning: population mean is less than some value
Or...
Ha: µ > ? -->meaning: population mean is greater than some value

Note: I am using a question mark in place of a specific value. Usually you will know what the value is depending on the information given in a problem.

I hope this will help and is what you were asking.