Question

Your research supervisor wants you to test the null hypothesis H₀: μ = 50 against the one-sided alternative hypothesis H_a: μ > 50. The population has a normal distribution with a standard deviation of 12.0. You are told to use a sample size of 121 and a rejection region of x bar > 52 .

a) What is the power of this test of significance under the alternative hypothesis that the mean  μ  is 53 .  State your answer to four digits to the right of the decimal point:

b) what is the probability of a type one error?

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	50
std deviation   =σ=	12.000
sample size       =n=	121
std error=σx̅=σ/√n=	1.09091

  power of this t

probability =P(X>52 |mean =53)=P(Z>(52-53)/1.091)=P(Z>-0.92)=1-P(Z<-0.92)=1-0.1797=0.8203

(please try 0.8212 if this comes wrong)
b)

probability(type I error) =P(X>52 |mean =50)=P(Z>(52-50)/1.091)=P(Z>1.83)=1-P(Z<1.83)=1-0.9666=0.0334

(please try 0.0336 if this comes wrong)