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A company wants to test if average weekly demand is more than 2000 lbs. Test is to be carried out at 5% level of significance, and an estimate of the population variance is 1,000,000. What is the power of the test if the true mean is 2300 lbs.

So here is the sol'n (u represents population mean, and x represents x bar, sample mean, z is z-score, based on 5% is 1.645):

Hypothesis statement: Null: u <= 2000 Alternative: u > 2000

xcritical = u + zo (o is standard deviation, calculation shows it to be 200)

xcritical = 2000 + 1.645(200)

xcritical = 2349

Power at 2300

P(xcritical > 2349) = P (z > 0.145)

P(z > 0.145) = 0.5 - 0.0596 = 0.4404

So the thing i dont understand, is that if the power of the test is the probability of correctly rejecting the null hypothesis when it is false, why do we calculate the area beyond the z-score and call that the power of the test. Isnt the area beyond supposed to be Beta, the probability of making a type II error?

Any help is greatly appreciated