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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: \mu =5.0 volt versus H1: \mu !=5.0 volt, by using sample size n=8. a) If the H0 acceptance range is 4.85 <= ???? <= 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 ???? is outside of the acceptance range. b) Find the testing power (1-\beta ) for detecting a true mean output voltage of 5.1 volts. c) 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?