A psychologist is studying the self image of smokers, as measured by the self-image (SI) score from a personality inventory. She would like to examine the mean SI score, ?, for the population of all smokers. Previously published studies have indicated that the mean SI score for the population of all smokers is 82 and that the standard deviation is 15, but the psychologist has good reason to believe that the value for the mean has decreased. She plans to perform a statistical test. She takes a random sample of SI scores for smokers and computes the sample mean to be 76.
Based on this information, complete the parts below.