Question

Participation in organized social activities (e.g., sports, clubs/groups) seems to improve self-esteem in adolescents. In one study, a sample of 64 adolescents with a history of group participation are given a self-esteem questionnaire. Researchers already know that the scores on this questionnaire are normally distributed and that the general population of adolescents have a mean score of µ = 55 and σ = 12. The sample produces a mean score of M = 52. Perform a two-tailed z-test with an alpha of .05; round your final answer to two decimal places, and show all of your calculations for full credit.

Answer 1

Solution :

This is the two tailed test,  

The null and alternative hypothesis is ,

H0 :   = 55

Ha :    55

Test statistic = z

= (M - ) / / n

= (52 - 55) / 12 / 64

Test statistic = z = -2.00