2. A theory predicts that the mean age of stars within a particular type of star cluster is 3.3 billion years, with a standard deviation of .4 billion years. (Their ages are approximately normally distributed.) You think the mean age is actually greater, and that this would lend support to an alternative theory about how the clusters were formed. You use a computer to randomly select the coordinates of 50 stars from the catalog of known stars of the type you're studying and you estimate their ages. You find that the mean age of stars in your sample is 3.4 billion years. A. To test whether the population mean is greater than 3.3 billion years, what would your null and alternative hypotheses be? Be sure to state the hypotheses in the context of the problem. (2 points) B. What test would you plan to use, how will the test work, and what are the conditions necessary to use the test? Does your situation meet those conditions? (2 points) C. Calculate your test statistic and P-value. Show your work, including the formulas you use to calculate the statistic. (2 points) D. What's your conclusion using = .05? (2 points)