Question

Locus of Control has μ = 106 and σ =12. Test whether ARC students (n = 36, M = 109) differ on Locus of Control. α = .05.

1. σ_{M =}

Answer 1

Solution:
Given in the question
Locus of Control has
Mean() = 106
Standard deviation() = 12
We need to test wheter ARC Students differs on Locus of control so null and alternative hypothesis can be written as
Null hypothesis H0: = 106
Alternate hypothesis Ha: 106
Sample size (n) = 36
Sample mean (Xbar) = 109
M = /sqrt(n) = 12/sqrt(36) = 2
Here we will use Standard normal table as Population standard deviation is known and sample size is large enough so test stat value can be calculated as
Z test stat = (Xbar - )//sqrt(n) = (109-106)/12/sqrt(36) = 1.5
at alpha = 0.05, and this is two tailed test so from Z table we found Zcritical value = +/-1.96
Decision Rule: Reject H0, if Test stat value is less than -1.96 or test stat value is greater than 1.96, else do not reject the null hypothesis.
Here we can see that test stat value is between 1.96 and -1.96. So we are failed to reject the null hypothesis. And we dont have significant evidence to support the claim that ARC Students differs on Locus of control.