A psychologist is studying the self image of smokers, as measured by the self-image (SI) score from a personality inventory.

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 and that the standard deviation is , but the psychologist believes that the value for the mean has increased. She plans to perform a statistical test. She takes a random sample of SI scores for smokers and computes the sample mean to be .