Question

A two-sided hypothesis test is being conducted for testing the mean of a normal distribution at the 85% level. The hypothesized mean value is 84 whereas the true mean is 86 with the variance being equal for both the hypothesized and real distributions at the value of 17.20. The sample size is 10. 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? A)0.15, 0.4644, 0.5356 B)0.4644, 0.15, 0.85 C)0.4644, 0.15, 0.15 D)0.5960, 0.15, 0.15 E)0.5960, 0.15, 0.4040 D)0.15, 0.5960, 0.4040 E)0.4644, 0.15, 0.5356 F)0.5960, 0.15, 0.85

Answer 1

sample size    n=		10
std deviation σ=		4.147
std error ='σx=σ/√n=4.14728827066554/√10=		1.3115

for 0.15 level with two tail test , critical z=

1.440

(from excel:normsinv(0.075)

rejection region: μ-Zα*σx <Xbar >μ+Zα*σx or 82.112<Xbar>85.888

P(Type II error) =P(82.112<Xbar<85.888|μ=86)=P(82.112-86)/1.311<z<(85.888-86)/1.311)=P(-2.96<z<-0.09)=0.4644

alpha =1-0.85 =0.15

power =1-type II error =0.5356

E)0.4644, 0.15, 0.5356