Research data indicates that adolescents especially adolesce

Research data indicates 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 = 12, the researcher want to test whether or not this result is sufficient to conclude that self-esteem for adolescent girls is significantly different from self-esteem for pre-teen girls. Use a two-tailed test with = .05.

(1) What type of statistical analysis should be run to address this question?

(2) What are the assumptions of your chosen statistical test?

(3) Identify the null and alternative/research hypotheses in both words and symbols.

(4) Calculate the test statistic that will help you answer this question.

(5) Identify the critical value(s) for your statistical test and compare it to your obtained test statistic.

(6) Draw conclusion regarding the null hypothesis and the subject matter.

(7) Write the statistical information from your test in APA format.         

Solution

Set Up Hypothesis
Null, result is sufficient to conclude no diffrence H0: U=75
Alternate, result is sufficient to conclude significantly different from self-esteem H1: U!=75
Test Statistic
Population Mean(U)=75
Given That X(Mean)=66
Standard Deviation(S.D)=12
Number (n)=9
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=66-75/(12/Sqrt(9)
Zo =-2.25
| Zo | =2.25
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =2.25 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != -2.25 ) = 0.0244
Hence Value of P0.05 > 0.0244, Here we Reject Ho

result is sufficient to conclude significantly different from self-esteem