Question

The average height (u) of a population of fifth-graders is u = 60 inches, and the standard deviation (o) equals 5.0 inches. You plan to randomly sample N fifth-graders from a population, measure each child's height, compute X, and conduct the following two-sided hypothesis test: Ho: = 59 inches Ha: #59 inches Decide which scenario below leads to the larger Type II Error (all other factors being equal): 1. N=75 OR N=25 II. a=0.01 OR a=0.05 OI) N=25 II) a=0.01 OI) N=75 l) a=0,01 I) N=75 II) -0,05 Cannot be Determined OI) N=25 II) -0.05

Answer 1

I) Greater the sample size, decreases both the type I error as well as type II error. Therefore we would have a larger type II error for a smaller sample size for N = 25 here.

II) There is a trade off between the type I error and the type II error. Therefore greater the type I error, smaller would be the type II error, while smaller the type I error, greater would be the type II error. Therefore 0.01 level of significance will have a greater Type II error here.

Therefore N = 25 and 0.01 level of significance is the correct answer here.