Childhood participation in sports, cultural groups, and youth groups appears to be related to improved selfesteem for adolescents (McGee, Williams, Howden-Chapman, Martin, & Karachi, 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 μ – 50 and a standard deviation of σ = 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-eastern scores for these adolescents are significantly different from those of the general population? Use a two-tailed test with α – .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.
Samples mean (M) is given as 53.8, population mean is given as 50, standard deviation is given as 15, alpha level is given as 0.05 and sample size for male is given as 100.
The null hypothesis states that there is no effect of the treatment and alternative hypothesis states opposite of null hypothesis. As given in the question that population mean is 50 and two tailed test is used, so the null hypothesis and alternative hypothesis for this question are:
The alpha level is given in the question as 0.05 and need to find boundaries of the critical region. As given in the question that two tailed hypothesis test used, so acceptance region is:
The z-score critical value at 0.975 or at is using the z table
To Compute: The Cohen’s d to estimate the size of the difference.
To Demonstrate: The results of the hypothesis test and the measure of effect size would appear in research report.
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