Question

A dean in the business school claims that GMAT scores of applicants to the school’s MBA program have decreased during the past 5 years. Five years ago, the mean and standard deviation of GMAT scores of MBA applicants were 580 and 60, respectively. A random sample of 30 applications for this year’s program were selected and the GMAT scores recorded. Find the power of the hypothesis test when, in fact, the true mean GMAT score is 550. Take α = 0.04, and assume the population standard deviation has remained the same

Answer 1

true mean ,    µ =    550              
                      
hypothesis mean,   µo =    580              
significance level,   α =    0.04              
sample size,   n =   30           0.3125  
std dev,   σ =    60.0000              
                      
δ=   µ - µo =    -30              
                      
std error of mean,   σx = σ/√n =    60.0000   / √    30   =   10.95445

Zα =       -1.7507   (left tail test)

P(type II error) , ß =   P(Z > Zα - δ/σx)                  
= P(Z >    -1.751   - (   -30   /   10.9545   ))
=P(Z>    0.988   ) =   0.1616   [ Excel function: =1-normsdist(z) ]      

power =    1 - ß =   0.83841