Question

Childhood participation in sports, cultural groups, and youth groups appears to be related to improved self-esteem for adolescents. 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 μ = 40 and σ = 12. The sample of group-participation adolescents had an average of  X=43.36. Does this sample provide enough evidence to suggest that self-esteem scores for group-participation adolescents are higher than those of the general population?

Carry out a hypothesis test using a=0.01.

(A)\State the null hypothesis and alternative hypothesis.

(B)Calculate the p-value. Show your steps.

(C)What is your decision regarding the two hypotheses?

Answer 1

This is the right tailed test .

The null and alternative hypothesis is

H₀ : = 40

H_a : > 40

Test statistic = z

= ( - ) /    / n

= (43.36 - 40) / 12 / 100

Test statistic = 2.8

P(z > 2.8) = 1 - P(z < 2.8) = 0.0026

P-value = 0.0026

P-value <

Reject the null hypothesis .

There is enough evidence to conclude that the self-esteem scores for group-participation adolescents are higher than those of the general population .