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Statistics: Using an interval ratio to analyze self esteem f

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5. 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. She gives them a 50-item self-esteem inventory before they begin playing sports and administers it again after six 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 appear below.

Before After
44 46
40 41
39 41
46 47
42 43
43 45

6. The student in Question 5 above decides to conduct the same study using a within-participants design in order to control for differences in cognitive ability. He selects a random sample of participants and has them study different material of equal difficulty in both the music and no music conditions. The data appear below. As before, they are measured on an interval-ratio scale and are normally distributed.

Music No Music

6 10
7 7
6 8
5 7
6 7
8 9
8 8

a. What statistical test should be used to analyze these data?
b. Identify H0 and Ha for this study.
c. Conduct the appropriate analysis.
d. Should H0 be rejected? What should the researcher conclude?
e. If significant, compute the effect size and interpret.
f. If significant, draw a graph representing the data.

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