Refer to the Journal of Statistics Education data on diamonds saved in the file. In Exercise 6.122 you selected a random sample of 30 diamonds from the 308 diamonds and found the mean and standard deviation of the number of carats per diamond for the sample. Let m represent the mean number of carats in the population of 308 diamonds. Suppose you want to test H0: μ = .6 against Ha: μ ≠ .6.
a. In the words of the problem, define a Type I error and a Type II error.
b. Use the sample information to conduct the test at a significance level of α = .05.
c. Conduct the test, part b, using a = .10.
d. What do the results suggest about the choice of α in a test of hypothesis?