Suppose you are the quality control manager of a battery company. It is known that the lifetime of all the batteries is normally distributed. You have selected a sample of 15 batteries. You found the mean lifetime of the 15 batteries is 58 hours and the standard deviation of this sample is 10 hours. Construct a 90% confidence interval for mean lifetime of all the batteries in the company.(You can use Excel to answer this question, but you need to show the formulas whenever possible.)

(b) If the sample size increases, will the confidence interval become wider or narrower?

(c) Is a 90% confidence interval wider or narrower than a 95% confidence interval?