A twosided 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 
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: μZα*σx <Xbar >μ+Zα*σx or 59.008<Xbar>62.992  
P(Type II error) =P(59.008<Xbar<62.992μ=66)=P(59.00866)/1.211<z<(62.99266)/1.211)=P(5.77<z<2.48)=0.0065 
alpha =10.90 =0.10
power =1type II error =0.9935
Correct option is: 0.0065, 0.10, 0.9935
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