Medical researchers have developed a new artificial heart constructed primarily of titanium and plastic. The heart will last and operate almost indefinitely once it is implanted in the patient's body, but the battery pack needs to be recharged about every four hours. A random sample of 50 battery packs is selected and subjected to a life test. The average life of these batteries is 4.05 hours. Assume that battery life is normally distributed with standard deviation equal to 0.2 hours. Analysts wish to test the hypothesis that the mean life of battery packs is bigger than 4 hours. Using Type I error probability = 0.05,
A) What is the numerical value of the test statistic taken to two decimal places?
B) What is the p-value for the hypothesis test of part A?
C) If the true population mean is 4.03 hours, what is the value of beta, the probability of Type II error? Answer to three decimal places.