You are managing an engineering development of a new engine, code named Astral. Your company is considering replacing its existing engine, the Dominion, with the Astral, if the new tests show Astral is better. Better in this case is a lower failure rate. Astral represents a leap in new technology and if the R&D is promising, you will make the decision to invest heavily in new development. If the R&D does not indicate Astral will work, you need to decide to pull the plug on Astral, and stick with the Dominion. Each new Astral engine is manufactured, tested, and designated a success or a failure. You want to very sure that you are making a good decision here, so you want to use an of 0.01. Your management team has decided that an engine failure rate of up to a certain level for the Astral is acceptable. Astral: failure rate between 0% and 9% is acceptable Dominion: current failure rate is 9% If your initial tests lead you to believe the Astral failure rates will be lower than the Dominion, you can proceed with development of Astral. However, if the tests lead you to believe the Astral engine failure rates will be too high, you need to scratch the Astral project and stick with the Dominion. For this, you are welcome to use our Excel template. If you do this, please include all your work, including Excel sheets with numbers in them. Label everything to make it easy to find. 1. What sort of hypothesis testing situation is this? Population mean or proportion? Sigma known or unknown? 2. Formulate a null and an alternative hypothesis. Tell me why you chose the hypotheses you did. 3. What would be a Type I and a Type II error based on your hypotheses? 4. First batch: Your research team built and tested the first batch of the engines. You have the results in the Batch 1 tab. Based on the first batch of tests, conduct a hypothesis test and tell us what is your conclusion? Would you move forward with the Astral based on these tests? 5. Your boss didn't like the results or conclusions of the first batch. She called for another test, the second batch. The results are in the Batch 2 tab. Assume the second batch of results is completely independent of the first batch (i.e. there is no overlap in the data sets.) Based on the second batch of tests, conduct a hypothesis test and tell us: what is your conclusion now? Would you move forward with Astral? 6. Your boss says, "I'm having trouble reconciling the results from Batch 1 and Batch 2. I'm going to call for a third study, this one with a sample size of 500 Astral units. What is the biggest number of failures we can afford to have in this third study (let's call it Batch 3) and still decide to move forward with the Astral manufacture?" 7. They want to know one more question. "We've run Batch 4 of tests, and we've had four Astral engines fail. (Batch 4 is independent of Batches 1, 2, and 3.) How big does Batch 4 need to be for us to still conclude we should move forward with Astral?"