An electronics firm mass produces a component for which there is a standard measure of quality. Based on testing vast numbers of these components, the company has found that the average quality is μ = 232 with σ = 4. However, in recent years the quality has not been checked, so management asks you to check its claim with the goal of being reasonably certain that an average quality of less than 232 can be ruled out. That is, assume the quality is poor and in fact less than 232 with the goal of empirically establishing that this assumption is unlikely. You get

¯X

= 240 based on a sample n = 25 components, and you want the probability of a Type I error to be .01. State the null hypothesis and perform the appropriate test assuming normality and σ = 4.

11. An antipollution device for cars is claimed to have an average effectiveness of exactly 546. Based on a test of 20 such devices, you find that

¯X

= 565. Assuming normality and that σ = 40, would you rule out the claim with a Type I error probability of 0.05?