The mean income per person in the United States is $40,500, and the distribution of incomes follows a normal distribution. A random sample of 18 residents of Wilmington, Delaware, had a mean of $51,500 with a standard deviation of $10,200. At the 0.050 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?

a. State the null hypothesis and the alternate hypothesis.

b. State the decision rule for 0.050 significance level. (Round your answer to 3 decimal places.)

c. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

d. Is there enough evidence to substantiate that residents of Wilmington, Delaware, have more income than the national average at the 0.050 significance level?