The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is at least 11.52 inches. Ten cities in the northeast are randomly selected and the mean rainfall amount is calculated to be 7.42 inches with a standard deviation of 1.3 inches. At the = 0.05 level, can it be concluded that the mean rainfall was below the reported average? What if = 0.01? Assume the amount of summer rainfall follows a normal distribution.

a. State the null and alternate hypothesis.

b. State the p-value.

c. State alpha.

d. What is the decision?

e. Make a conclusion.

f. Answer any other questions asked in the problem

Set up the hypothesis test, find the p-value, sketch the graph and state the conclusion.

(With a step-by-step explanation please.)