During the winter of 2012– 2013, the average utility bill for Delaware residents was $ 186 per month. A random sample of 40 customers was selected during the winter of 2013– 2014, and the average bill was found to be $ 178.10 with a sample standard deviation of $ 22.40.

a. Using σ = 0.05, does this sample provide enough evidence to conclude that the average utility bill in Delaware was lower in the winter of 2013– 2014 than it was in the winter of 2012– 2013?

b. Does changing the value of a from 0.05 to 0.01 affect your conclusion? Why or why not?

c. Use PHStat to validate these results and to determine the p value for this test.