8 (50pts) Due 10/27 1. (This is also the Sweetening cola example in topic 8): calculating power. The cola maker wants to test at the 5% significance level the following hypotheses: H0: = 0 versus Ha: > 0 Ten taste scores were used for the significance test. The distribution of taste scores is assumed to be roughly Normal with standard deviation = 1. We want to calculate the power of this test when the true mean sweetness loss is = 0.8. (a) What values of the z statistic would lead us to reject H0? To what values of do they correspond? Use the inverse Normal calculations to figure this out. (b) When the true mean sweetness loss is = 0.8, how often would we reject H0? That is, what is the probability of obtaining sample averages like the ones defined in (a) when = 0.8? Use the z table to calculate this probability. This probability is the power of your test against the alternative = 0.8, the probability of rejecting H0 when the alternative = 0.8 is true. 2. In order to test a hypothesis Ho: =5 Ha: <5 42.74772255