Question

an example scenario of how organizations use difference in population means in hypothesis testing before making decisions

Answer 1

The hypothesis test for difference is population means is applied to compare whether the average difference between two groups is really significant or if it is due instead to random chance.

For example, in a packing plant, a machine packs cartons with jars. It is supposed that a new machine will pack faster on the average than the machine currently used. To test that hypothesis, the times it takes each machine to pack ten cartons are recorded. Do the data provide sufficient evidence to conclude that, on the average, the new machine packs faster?

Here null and alternative hypothesis will be

H₀: µ₁ – µ₂ = 0          (difference in population means is same)

H₁: µ₁ – µ₂ > 0          (difference in population means is positive; average of first sample (new machine) is higher)