Continuing from the gas example, if you are only concerned about gas stations are short selling customers, i.e., you will be happily silent if they pump 1.05 gallon and only charge for 1 gallon. Then, using the hypothesis terms, our H0 becomes mu >=1, H1: mu < 1..

Let us assume the volume of gas dispensed for one supposed gallon, denoted as X, follows normal distribution 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, whatare reject region and do not reject region this time using alpha=0.05, respectively? Draw the density function, identify the rejection non rejection region on the graph, and use excel for the calculation.