Question

Research data indicate that adolescents, especially adolescent girls, experience a drop in self-esteem. To evaluate this result, a researcher obtains a sample of n = 9 adolescent girls, all 13 years old. A self-esteem test is given to each participant and the average score for the sample is M = 66. It is known that the distribution of self-esteem scores for the population of pre-teen girls is normal with µ = 75. Assuming that the population standard deviation is σ = 12, is this result sufficient to conclude that self-esteem for adolescent girls is significantly different from self-esteem for pre-teen girls? Use a two-tailed hypothesis test with α = .05.

Must show the four steps and draw the normal curve to identify the critical regions.

Answer 1

1)

H0: = 75

Ha: 75

2)

Test statistics

z = ( - ) / ( / sqrt(n) )

= ( 66 - 75) / ( 12 / sqrt(9))

= -2.25

3)

Critical values at 0.05 level = -1.96 , 1.96 (From Z table)

Since test statistics falls in rejection region, Reject H0.

Shaded region is rejection region.

4)

Conclusion - We have sufficient evidence to support the claim .