2. Use this scenario to answer the following questions.
Colored Wax & Co. sells candles with a mean burn time of 50 minutes. The company
wants to test its candles' burn time against a competitor's candles. Researchers from
Colored Wax & Co. randomly select 25 candles from its competitor for testing. From
previous research, the staff of Colored Wax & Co. knows that σ = 12.5 .
A. Colored Wax & Co. wants to test a two-sided alternative hypothesis with α =
.05. What are the null and alternative hypotheses for this test?
B. What's the probability of a Type I error in this test?
C. Describe a Type I error for H0 : µ = 50.
D. What is the rejection region (for what values of x will H0 be rejected) for
H0 : µ = 50?
E. Describe a Type II error for H0 : µ = 50.
F. Suppose the mean burn time is actually 53 minutes. Find the possibility of a
Type II error (β) and the power of the test.