Question: A developmental psychologist would like to determine if depression is affected by age. It is known that the general population averages a mean of 50 and a standard deviation of 10 on a standardized test of depression. The psychologist wished to see if seniors (age greater than or equal to 65) have greater depression on average than the general population. Assuming that depression scores are normally distributed and that the standard deviation remains 10 for seniors, how large a sample must she use to test her directional hypothesis if she wants the probability of a Type I error, alpha to be .01 and she wants the probability of a Type 2 error, Beta to be .05 when Mean1 =65?