Medical researchers have developed a new artificial heart co

Medical researchers have developed a new artificial heart constructed primarily of titanium and plastic. The heart will last and operate almost indefinitely once implanted in the patient’s body, but the battery pack needs to be recharged every 4 hours. A random sample of 50 battery packs is selected and subjected to a life test. The average life of these batteries is 4.10 hours. Assume that battery life is normally distributed with standard deviation of 0.2 hours. Is there evidence to support the claim that mean battery life exceeds 4 hours? Use a significance level = 0.01.

a) (1 pt.) Are the normality assumptions satisfied? Explain why.

b) (1 pt.)State hypotheses

c) (1 pt.)Calculate the test statistic

d) (1 pt.)What is/are the critical value(s)?

e) (1 pt.)What is your decision?

f) (1 pt.)What is the conclusion/interpretation of this decision?

g) (1 pt.)Calculate the p-value for this test.

h) (2 pts.)Suppose the developers need to detect a difference of 0.05 hours at = 0.01. How powerful is this test? i) (2 pts.)What sample size would be needed to detect the difference of 0.05 hours at = 0.01 and power of 85%?

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