A researcher is interested in whether participating in sports positively influences self-esteem in young girls. She identifies a group of girls who have not played sports before but are now planning to begin participating in organized sports. The researcher gives them a 50-item self-esteem inventory before they begin playing sports and administers the same test again after 6 months of playing sports. The self-esteem inventory is measured on an interval scale, with higher numbers indicating higher self-esteem. In addition, scores on the inventory are normally distributed. The scores follow.

Before                                                                  After

44……………………………………………………………….46

40……………………………………………………………….41

39……………………………………………………………….41

46……………………………………………………………….47

42……………………………………………………………….43

43……………………………………………………………….45

a. What statistical test should be used to analyze these data?

b. Identify H₀ and H_a for this study.

c. Conduct the appropriate analysis.

d. Should H₀ be rejected? What should the researcher conclude?

e. If significant, compute and interpret the effect size.

f. If significant, draw a graph representing the data.

g. Determine the 95% confidence interval.