When the manufacturing process is working properly, AlwaysReady flashlights have lifetimes that follow a slightly right-skewed distribution with hours. A quality control supervisor selects a simple random sample of n flashlights every hour from the production line and measures the lifetime of each. If she is convinced that the mean lifetime of all batteries produced that hour is less than 22 hours at the 5% significance level, then all those batteries are discarded.

Part A Define the parameter of interest and state appropriate hypotheses for the quality control supervisor to test.

Part B Since testing the lifetime of a battery requires draining the battery completely, the supervisor wants to sample as few batteries as possible from each hour's production. She is considering a sample size of n = 10. Is this an appropriate sample size? Why or why not?

Part C Describe a Type I and a Type II error in this situation and the consequences of each. A definition of Type I and Type II errors will earn zero points.

Part D The quality control officer is considering changing the significance level of the test to 1%. Discuss the impact this might have on error probabilities and the power of the test, and describe the practical consequences of this change.