A random sample of 50 batteries is selected and subjected to a life test. We found the following life time, in hours: 3.64 3.77 3.92 3.98 4.01 4.04 4.08 4.12 4.2 4.38 3.67 3.82 3.92 3.99 4.02 4.04 4.09 4.15 4.2 4.4 3.73 3.84 3.95 3.99 4.02 4.05 4.1 4.16 4.25 4.44 3.75 3.87 3.95 3.99 4.03Required:a. Design a test to support the claim that the mean battery life exceeds 4 hours, with a level of significance of α = 0.05. b. What is the null distribution? c. What is the acceptance region and the P-value? d. Is there enough evidence to support the claim? e. Construct, from the sample, a one-sided (lower bound) confidence interval for the mean μ. Compare your results with the claim.