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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

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.

a.

To determine
Whether the sample provide enough evidence to conclude that self esteem scores for these adolescents are significantly different from those of the general population or not.

Explanation

Given info:

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.

Justification:

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:

H0:μ=50H1:μ50

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:

p=1α2=10.052=10.025=0.975

The z-score critical value at 0.975 or at α=0.05 is ±1.96 using the z table

b.

To determine

To Compute: The Cohen’s d to estimate the size of the difference.

c.

To determine

To Demonstrate: The results of the hypothesis test and the measure of effect size would appear in research report.

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