Question

Tony Stark is developing a new model of the Iron Man suit. His previous suit model uses an average of 222.4 kilowatts per second, and he wishes to see if his new model is more efficient in other words, if the mean kW/s used is lower than the previous model). He takes a sample of five randomly selected suits made under the new model and finds that the mean amount of energy used is 210.2 kW/s with a standard deviation of 9.9 kW/s. He knows that the amount of energy used per second for a given suit follows a normal distribution. 1. Define the parameter of interest, including the proper symbol. 2. Define the appropriate hypotheses. 3. State and check the necessary assumptions. 4. Compute the test statistic. 5. When conducting hypothesis test, all of your steps up to and including) finding the test statistic will be identical, regardless of which approach you use. You then have a choice about how you complete the test. Tony wishes to know whether there is evidence at the 2% level that the new suit is more efficient. (a) P-Value Approach: Compute the p-value, using the appropriate probability notation. (b) Provide support for your decision regarding the null hypothesis using Part (a). (c) Rejection Region Approach: Find the rejection region. It may be helpful to include a sketch. (d) Provide support for your decision regarding the null hypothesis using Part (c). 6. Your decisions in Parts (b) and (d) above should match, leading you to the same conclusion even though you used different methods! Provide a summary statement in context of the problem.

Answer 1