If \(\mu\) is the population mean, which of the following is NOT a valid pair of null hypothesis \(H_0\) and alternative hypothesis \(H_1\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(H_0: \mu \ne 50\), \(H_1: \mu = 50\)
The null hypothesis always contains the equality: it uses =, ≤ or ≥. The alternative hypothesis states the difference: it uses ≠, > or <.
In Option (3) the signs are the other way round: \(H_0\) uses ≠ and \(H_1\) uses =. So this pair is not valid.
Options (1), (2) and (4) each have the equality in \(H_0\) and the opposite statement in \(H_1\), so they are valid pairs.