Chapter 9.7, Problem 193E

In Exercises 9.191–9.196, we have given a hypothesis testing situation and (i) the population standard deviation, σ, (ii) a significance level, (iii) a sample size, and (iv) some values of μ_a. For each exercise,

1. a. determine the probability of a Type I error.
2. b. apply Procedure 9.4 on page 425 to determine the probability of a Type II error for the first given value of μ_a.
3. c. apply Procedure 9.5 on page 427 to construct a power curve based on the given values of μ_a.

9.193 Iron Deficiency? The null and alternative hypotheses obtained in Exercise 9.17 on page 375 are, respectively,

H₀: μ = 18 mg

H_a: μ < 18 mg,

where μ is the mean iron intake (per day) of all adult females under the age of 51 years.

i. σ = 4.2

ii. α = 0.01

iii. n = 45

iv. μ_a = 15.50, 15.75, 16.00, 16.25, 16.50, 16.75, 17.00, 17.25, 17.50, 17.75