Question: A sample set of 30 scores has a mean equal to 82 and a standard deviation of 12. Can we reject the hypothesis that this sample is a random sample from a normal population with µ=85? Use α=0.01 2 tail in making your decision.  Edit

Answer: Null hypothesis: H0: µ=85
Alternative hypothesis: H1: µ≠85
Sample sd=12 , sample size,n=30
population sd= sqrt(n/n-1)*sample sd=sqrt(30/29)*12=12.205
z= (x bar - 82)/(12.205/sqrt(30))=(x bar - 82)/2.23
If x bar=85
z= (85-82)/2.23=3/2.23=1.34
at α=0.01 2 tail z-critical=+/-2.58
Z-calculated(1.34) So, fail to reject null.  Edit