Size of diamonds sold at retail. Refer to the Journal of

Chapter 7, Problem 124SE

(choose chapter or problem)

Size of diamonds sold at retail. Refer to the Journal of Statistics Education data on diamonds saved in the file. In Exercise 6.120 (p. 344) 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 \(\mu\) represent the mean number of carats in the population of 308 diamonds. Suppose you want to test \(H_{0}: \mu=.6\) against \(H_{\mathrm{a}}: \mu \neq .6\).

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 \(\alpha=.05\).

c. Conduct the test, part b, using \(\alpha=.10\).

d. What do the results suggest about the choice of \(\alpha\) in a test of hypothesis?

Text Transcription:

mu

H_0: mu = .6

H_a: mu neq .6

alpha = .05

alpha = .10

alpha