Hypothesis Testing and Power of Test

The manufacturer believes that the mean content of tubes produced by the manufacturing process is 126.5ml. However, after a period of time the manufacturer is concerned that the mean content may have slipped so he takes another sample, this time of 20 tubes, and observes the mean of the sample to be 126.2ml.

1) Perform a hypothesis test at 5% level to determine whether the sample provides any evidence that the mean of the manufacturing process is now less than 126.5ml (assume the standard deviation is unchanged at 0.6ml). Show clearly the null and alternative hypotheses for the test, the critical value and your conclusion as a result of the test.

2) If the true mean is 126ml, what is the power of test?

Re: Hypothesis Testing and Power of Test

My approach to this question is...

Null Hypothesis: mu = 126.5ml

Alternative Hypothesis: mu is less than 126.5ml

critical value is 1.645 because 5% level of test and is a 1 sided test.

z =( 126.2 - 126.5) / (0.6 / sqrt 20) = -2.236

-2.236 is lesser than -1.645 (insignificant)

Therefore, there is insufficient evidence that the mean of manufacturing process is less than 126.5ml.

Is this correct? Advices on the approach please?

Re: Hypothesis Testing and Power of Test

your Ho should be rejected since your sample z =-2.236 is within the rejection region z=-1.645