Type I error and Type II error:

1. In the past, the mean running time for a certain type of radio battery has been 9.8 hours. The manufacturer has introduced a change in the production method and wants to perform a significance test to determine whether the mean running time has increased as a result. The hypotheses are: H0: μ = 9.8 hours and Ha: μ > 9.8 hours

Explain the meaning of a Type I error.

A) Concluding that μ > 9.8 hours when in fact μ = 9.8 hours

B) Concluding that μ = 9.8 hours when in fact μ > 9.8 hours

C) Concluding that μ > 9.8 hours when in fact μ > 9.8 hours

D) Concluding that μ < 9.8 hours when in fact μ > 9.8 hours

E) Concluding that μ = 9.8 hours when in fact μ < 9.8 hours

2. A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer wants to perform a significance test to determine whether their suspicion is correct. The hypotheses are:

H0: μ = $1200

Ha: μ > $1200

Suppose that the results of the sample lead to rejection of the null hypothesis. Classify that conclusion as a

Type I error, a Type II error, or a correct decision, if in fact the average fee charged by the clinic is $1200

3. It is desired to test H0: p = 0.5 against Ha: p < 0.50 using α = 0.05. If truly p = 0.4, what is the probability of a type II error if n = 150?