Question: After once again losing a football game to the college's arch rival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. A SRS of 100 alumni from the population of all living alumni was taken. Fifty-nine of the alumni in the sample were in favor of firing the coach. Suppose you wish to gather evidence that the majority (more than 50%) of alumni are in favor of firing the coach. Assuming the assumptions for the appropriate test are met, show the steps in a hypothesis test and report your results at the 1% level of significance. Round to 4 decimals.