4.1 (Adapted from Gerstman 9.11, p. 212) Studies in the general population suggest that the gestational length of uncomplicated pregnancies vary according to a Normal distribution with mu=39 weeks and sigma=2 weeks. A sample of 28 babies born to teenagers demonstrates an average gestational length (x-bar) of 38.3 weeks. Test whether the mean gestation period in teenagers is significantly different from the expected value of 39 weeks. Use a two-sided alternative. Show all hypothesis testing steps. TOP OF PAGE 2 Problem 4.2 As a follow-up to 4.1: a) If you did the test with a one-sided alternative, that the mean gestational length in teens is shorter than in the general population, would the power increase or decrease? Defend your answer. (Hint- what would be the p-value/conclusion for a 1-sided test using the same data as problem 4.1?) b) Somebody rounded when they wrote down the value of sigma; the true value is sigma=2.2. If we use the unrounded value of sigma, would this increase or decrease the power of the test? (No need to do calculations, though they may help if you are stuck.) c) If the true mean gestation of teen pregnancies is 38.5 weeks, the actual power of the test in Problem 4.1 is around 0.26 (or 26%) when we use an alpha level (significance level) of 0.05. How can you use this information to interpret your non-significant (hint, hint) p-value in Problem 4.1