It is claimed that the mean height for Iowa women is different than the national average, which is 64.4". A SRS of 20 Iowa women had an average height of 66" and standard deviation of 2.8". Let 0 be the test statistic for testing the implied hypotheses.

Consider the three tests...

Test 1: Reject 0 if (0 2.1) is observed.

Test 2: Reject 0 if (0 2.5) is observed.

Test 3: Reject 0 if (0 2.1 or 0 2.1) is observed.

(a) Which test has the lowest Type I error probability?

(b) Which test has the lowest Type II error probability?

(c) Which test has the highest power?