Question

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 th e 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 an average of M = 53.8.

a. Does the 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 α = 0.05)

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 at it would appear in a research report.

Answer 1

In this question there are large sample size of 100, so we use z statistics for sentencing of hypotheisis.

(a) null hypothesis-there is no evidence to conclude that self steem scores for these adolescents are significantly different from those of general population.

        alternative hypo.-there is evidence to conclude that self steem scores for these adolescents are significantly different from those of general population.

     mu=50, sigma=15, n=100, xbar=53.8

    z=(xbar-mu)/ (sigma/sqrt(n))

    z=(53.8-50)/(15/sqrt(100))

    z=2.533333=calculated z statistics

     tabulated value of z statistics at 5% level of significance is 1.96

      calculated z statistics is greater than tabulated value of z statistics.

      So reject the null hypothesis. so there is evidence to conclude that self steem scores for these adolescents are significantly different from those of general population.

(b) d= (xbar-mu)/sigma

       d=(53.8-50)/15

        d=0.2533333

         if d is greater than 2, it is consider that size of difference is huge.

(c)    z=2.533333=calculated z statistics

     tabulated value of z statistics at 5% level of significance is 1.96

      calculated z statistics is greater than tabulated value of z statistics.

      So reject the null hypothesis. so there is evidence to conclude that self steem scores for these adolescents are significantly different from those of general population.