It is known that the average height of a man residing in the Canada is 174 cm and the standard deviation is 8 cm. Assume the heights are normally distributed. To test the hypothesis that men in your city are "average," a sample of 20 men have been chosen. The heights of the men in the sample follow:
a) Test the hypothesis at the significance level of a_{1} = 0.05
b) Test the hypothesis at the significance level of a_{2}= 0.01.
c) Find the p-value of the test, and use the p-value to verify your answers.