Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self- esteem for adolescents (McGee, Williams, Howden- Chapman, Martin, & Kawachi, 2006). In a representa- tive study, a sample of n = 100 adolescents with a history of group participation is given a standardized self-esteem questionnaire. For the general popula- tion of adolescents, scores on this questionnaire form a normal distribution with a mean of u = 50 and a standard deviation of o = = 15. The sample of group- participation adolescents had an average of M = 53.8. a. Does this sample provide enough evidence to con- clude that self-esteem scores for these adolescents are significantly different from those of the general nonul

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8. Childhood participation in sports, cultural groups, and youth groups appears to be related to improved 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 a mean of \(\mu = 50\) and a standard deviation of \(\sigma = 15\). The sample of group-participation adolescents had an average of \(M = 53.8\).

a. Does this sample provide enough evidence to conclude that self-esteem scores for these adolescents are significantly different from those of the general population? Use a two-tailed test with \(\alpha = .05\).

b. Compute Cohen's \(d\) to measure the size of the difference.

c. Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.
Transcribed Image Text:8. Childhood participation in sports, cultural groups, and youth groups appears to be related to improved 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 a mean of \(\mu = 50\) and a standard deviation of \(\sigma = 15\). The sample of group-participation adolescents had an average of \(M = 53.8\). a. Does this sample provide enough evidence to conclude that self-esteem scores for these adolescents are significantly different from those of the general population? Use a two-tailed test with \(\alpha = .05\). b. Compute Cohen's \(d\) to measure the size of the difference. c. Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.
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