A follow-up to the anorexia study of Example 6.4 plans a test of H0: = 0

A follow-up to the anorexia study of Example 6.4 plans a test of H0: μ = 0 against Ha: μ > 0, for the mean weight change μ for a new therapy, predicting that μ = 10.

The test uses α = 0.05.

For n = 30, suppose the standard deviation is 18. Find P(Type II error) if μ = 10 by showing

(a) a test statistic of t = 1.699 has a P-value of 0.05,

(b) we fail to reject H0 if ¯y < 5.6,

(c) this happens if ¯y falls more than 1.33 standard errors below 10,

(d) this happens with probability about 0.10.