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A company manufactures batteries that the CEO claims will last an average of 350 hours under normal use. A researcher randomly selected 20 batteries from the production line and tested these batteries. The tested batteries had a mean life span of 320 hours with a standard deviation of 50 hours. a) Construct 95% confidence interval for the battery life. Assume that the battery life follows Normal distribution. b) Construct 99% confidence interval for the battery life. (Assumption that the battery life follows Normal distribution is not valid). c) Write down the hypothesis to check the claim. d)Do we have enough evidence to suggest that the claim of an average lifetime of 350 hours is false? (Carry out hypothesis testing to check the claim at 5% significance level). Assume that the battery life follows Normal distribution. e)If the assumption that the battery life follows Normal distribution cannot be made, carry out the hypothesis testing procedure to check the claim.
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