22) A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1600 hours. A homeowner selects 90 bulbs and finds the mean lifetime to be 1580 hours with a population standard deviation of 50 hours. Test the manufacturer's claim. Use a = 0.05. a) Write the null and alternative hypotheses. Identify the claim . b) Determine if the test for this claim is a left-tailed, right-tailed, or two-tailed c) Find the p-value. Round to 4 decimal places. d) Reject or fail to reject the Ho? e) Intepret the decision for the original claim