The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 8 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. If required, round your answer to three decimal places.

(a) Show the sampling distribution of the sample mean annual rainfall for California.

E(x) _x California (b) Show the sampling distribution of the sample mean annual rainfall for New York.

E(x) _x New York (c) In which of the preceding two cases, part (a) or part (b), is the standard error of x smaller? Why?

The standard error is larger OR smaller for New York because the sample size is larger OR smaller than for California.

Can you please write out answer so I can see how it was worked out.