The null and alternative hypotheses for a test are H0: = 16.5 and Ha: = 16.5, respectively, where is the mean length

The null and alternative hypotheses for a test are H0: μ = 16.5 and Ha: μ = 16.5, respectively, where μ is the mean length of imprisonment for motor-vehicle-theft offenders in a city. Given below are

(i) the population standard deviation, σ, (ii) a significance level, (iii) a sample size, and (iv) some values of μ. Complete parts

(a) through

(c).

i. σ = 6.8 ii. α = 0.05 iii. n = 100 iv. μ = 15.50, 16.00, 17.00, 17.50

a. Determine the probability of a Type I error.

b. Construct a table that provides the probability of a Type II error and the power for each of the given values of μ.

c. Use the table obtained in part

(b) to draw the power curve.