I had recently conducted an experiment: the moment the fuel light in my car goes on, I will find a closest gas station to fill up the tank. But the number of gallons needed to fill up are all over the place. This makes me wonder how we can verify it is actually one gallon when the pump says it is one gallon, and maybe those gas stations that are always slightly cheaper are simply shorting their customers proportionally to gain a competitive edge.

conduct the following two hypothesis tests.

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.

Follow the same steps for discussions, draw your conclusions on each of these two questions.

Produce all your works in one excel file. You will need to allow your excel to save as "macro-enabled worksheet" to save your problem 2.