Suppose some researchers would like to investigate whether childhood participation in sports, cultural groups, and youth groups is related to improved self-esteem among adolescents. In a representative study, a sample of n = 100 adolescents with a history of group participation is given a standardized self-esteem questionnaire. For the general population of adolescents, scores on this questionnaire form a normal distribution with a mean of 40 and a standard deviation of 12 . A sample of adolescents who participated in group activities is obtained, and their average score on the questionnaire is 43.84. Does this sample provide evidence to conclude that self-esteem scores for group-participation adolescents are significantly different from those of the general population? Carry out a hypothesis test, showing all four steps. Use =.01 .

If the standard deviation in the above-described scenario had been , how would the results of the hypothesis test change? (Carry out the hypothesis test again, showing all four steps; use.)