Question

Q. If the population mean is 310, sample mean is 295, sample's standard deviation is 55, what is the power of the test (representing Type II error) for a sample size of 20? Apply the Type II error analysis with the operation curve below, and find out the power of the test? Does it match with the value you got from above? 1.0 0.8 0.6 0.4 0.2

Answer 1

Population Mean = 310. Sample Mean = 295; Sample Standard deviation = 55 ; Sample Size = 20

In a 2 tailed test, at 95 % probability( Alpha =0.05), Z = 1.96

i.e 1.96 = (X - 295) /( 55 / $\small \sqrt{20}$ )

X = 295 + 24.1048 = 319.105

Now, Values beyond 319.105 are rejected and less than 319.105 are accepted.

319.105 corresponds to Z of ( 319.105 - 310)/( 55 / $\small \sqrt{20}$ ) , i.e Z = 0.74

P(X<0.74) = 0.7704

Therefore, probability of Type 2 error, $\small \beta$ = 0.7704 = 77.04%

Power of test = 1 - $\small \beta$ =1- 77.04% = 22.96%