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?