A manufacturer is interested in the study of the output voltage of a power supply circuit used in a computer. The output voltage is assumed to be normally distributed with a nominal voltage of 5.0 volt and a standard deviation 0.25 volt. The manufacturer wishes to test a hypothesis H0: µ=5.0 volt versus H1: µ!=5.0 volt, by using sample size n=8.
If the H0 acceptance range is 4.85<=X ̅<=5.15, find \alpha =? Hint: \alpha is the probability that H0 is rejected given that H0 is true, or given the true mean is 5.0 but X ̅ is outside of the acceptance range.
Find the testing power (1-\beta ) for detecting a true mean output voltage of 5.1 volts.
If the manufacturer needs \alpha =0.05 and testing power 0.90 to detect a true mean output voltage of 5.1 volt, what sample size does he need to use?