Question

A two-sided hypothesis test is being conducted for testing the mean of a normal distribution at the 90% level. The hypothesized mean value is 61 whereas the true mean is 66 with the variance being equal for both the hypothesized and real distributions at the value of 13.20. The sample size is 9. What are the values of the following in the asked order: Pr(Failing to reject the null hypothesis when it is false), Pr(Rejecting the null hypothesis when it is true), the power of the hypothesis test?

answers:
	0.0079, 0.10, 0.90
	0.0065, 0.10, 0.10
	0.0079, 0.10, 0.9921
	0.10, 0.0079, 0.9921
	0.0079, 0.10, 0.10
	0.0065, 0.10, 0.90
	0.10, 0.0065, 0.9935
	0.0065, 0.10, 0.9935

Answer 1

for 0.1 level with two tail test , critical z=

1.645

(from excel:normsinv(0.05)

sample size    n=		9
std deviation σ=		3.633
std error ='σx=σ/√n=3.63318042491699/√9=		1.2111

rejection region: μ-Zα*σx <Xbar >μ+Zα*σx or 59.008<Xbar>62.992

P(Type II error) =P(59.008<Xbar<62.992|μ=66)=P(59.008-66)/1.211<z<(62.992-66)/1.211)=P(-5.77<z<-2.48)=0.0065

alpha =1-0.90 =0.10

power =1-type II error =0.9935

Correct option is: 0.0065, 0.10, 0.9935