Question

In a packing plant, one of the machines packs jars into a box. A sales rep for a packing machine manufacturer comes into the plant saying that a new machine he is selling will pack the jars faster than the old machine. To test this claim, each machine is timed for how long it takes to pack 10 cartons of jars at randomly chosen times. Given a 95% confidence interval of (3.08, 10.12) for the true difference in average times to pack the jars (old machine - new machine), what can you conclude from this interval

Answer 1

We are 95% sure that the true difference in time to pack the jars between the old machine and the new machine is between 3.08 and 10.12 minutes, that is, we are 95% sure that the new machine takes between 3.08 and 10.12 minutes less than the old machine to pack the jars.

Explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

95% confidence interval of (3.08, 10.12) for the true difference in average times to pack the jars (old machine - new machine).

We are 95% sure that the true difference in time to pack the jars between the old machine and the new machine is between 3.08 and 10.12 minutes, that is, we are 95% sure that the new machine takes between 3.08 and 10.12 minutes less than the old machine to pack the jars.