Hypothesis Testing

Question

A sales manager believes that the mean number of days per year her company’s sales representatives spend traveling is less than 50. A test is made of H₀: μ = 50 versus H₁: μ < 50. The null hypothesis is not rejected. State an appropriate conclusion.

Answer 1

Maybe think of hypothesis testing as like a criminal trial. The null hypothesis is the presumption of innocence. The prosecutor wants to test that hypothesis, by arguing the defendant is guilty.

Maybe it's a tax evasion trial. The null hypothesis is that the taxpayer correctly claimed tax credits of $50. But the prosecutor believes deductions were less than $50. When the evidence is presented it shows insufficient evidence that the deductions were overstated. The presumption of innocence is not rejected. The defendant is acquitted of tax evasion.

The conclusion is 50 as the correct number of days is not rejected. It's not proven, just not rejected. Evidence is insufficient to reject it. It's similar to Robert Mueller saying he didn't exonerate Trump, just that there was insufficient evidence to indict. So the presumption of innocence is not rejected.