Historically, Shop-Mart has gotten an average of 2000 hours of use from its G&E fluorescent lightbulbs. Because its fixtures are attached to the ceiling, the bulbs are rather cumbersome to replace, and Shop-Mart is looking into the possibility of switching to Phipps bulbs, which cost the same. A sample of Phipps bulbs lasted an average of 2080 hours, and the p-value in a right-tail test (H0: μ ≤ 2000 versus H1: μ > 2000) is 0.012. Shop-Mart has shared these results with both G&E and Phipps.
a. Give Shop-Mart a recommendation. In doing so, use “0.012” in a sentence that would be understood by a Shop-Mart executive who has had no statistical training but is comfortable with probabilities as used by weather forecasters.
b. In interpreting these results, what level of significance might G&E like to use in reaching a conclusion? Explain.
c. In interpreting these results, what level of significance might Phipps like to use in reaching a conclusion? Explain.
d. If the test had been two-tail (i.e., H0: μ = 2000 versus H1: μ ≠ 2000) instead of right-tail, would the p-value still be 0.012? If not, what would the p-value be? Explain.