It is theorized that the systolic blood pressure of executives at a top hedge fu

Question

It is theorized that the systolic blood pressure of executives at a top hedge fund company have high blood pressures due to stress at work. A random sample of 72 executives had their blood pressures measured. The hypotheses are H0 : µ = 128 and Ha : µ > 128. Assume that the population standard deviation is = 15, and we want to conduct a hypothesis test at 0.02 significance level. If the mean blood pressure of all executives is 133, what is the power of this hypothesis test? As you work through this question, be sure to address the following:

(c) How likely are we to obtain values of the sample mean from the previous part if the mean blood pressure is truly 133? (This gives the power of the test).

Explanation / Answer

here for 0.02 level ; critical value z=2.0537

here std error of mean =/(n)1/2 =15/(72)1/2 =1.7678

hence crtitical value for rejection =mean +z*std error =128+2.0537*1.7678=131.6305

power of the test is probability of getting above value or higher then if true mean is 133

hence power of the test =P(X>131.6305)=1-P(X<131.6305)=1-P(Z<(131.6305-133)/1.7678)=1-P(Z<-0.7747)

=1-0.2193 =0.7807

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