Childhood participation in sports, cultural groups, and youth groups appears to be related to self-esteem for adolescents (McGee, Williams, Howden-Chapman, Martin, & Kawachi, 2006). 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 mu – 40 and 0 – 12 and . The sample of group participants has an average of M = 43.84. (17 points total) Would the researcher conduct a one-tailed or two-tailed hypothesis test? Explain why. (2 points) b) Use the information above to conduct a hypothesis test using . Be sure you complete all five steps of hypothesis testing and show your work/answers for each step. State your hypotheses using both words and statistical notation (2 points) Calculate standard error Correct equation (1 point) Correct value (1 point) Determine the critical value (1 point) Conduct hypothesis test Correct equation (1 point) Correct value (1 point) Comparison of obtained z and critical z (1 point) Make a decision about rejecting/failing to reject the hypothesis Explicitly states “reject” or “fail to reject” (1 point) Writes a 1-2 sentence conclusion interpreting the results (1 point) Writes correct conclusion using statistical notation (1 point) c) Calculate a 99% confidence interval for the above sample (4 points) Uses correct equation for lower CI value (1 point) Computes correct lower CI value (1 point) Uses correct equation for higher CI value (1 point) Computes correct higher CI value (1 point)