Let us assume the volume of gas dispensed for one supposed gallon, denoted as X, follows an unknown distribution but with a known sigma=0.02. And you decide to use X_bar out of 30 measures of one supposed gallon as the test statistic so to enjoy the benefit of central limit theorem.

We collected a sample of 30 measurements of one gallon gas, and we get X_bar = 1.1021.

1. We are interested to know whether the machine is properly calibrated, H0: mu=1, H1: mu not equal to 1.

2. We are interested to know whether the pump is adjusted intentionally to short customer: H0: mu>=1, H1: mu <1.

Produce all your works in one excel file. You will need to allow your excel to save as "macro-enabled worksheet" to save