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10_( 15 Points) A manufacturer claims that the mean lifetime of fluorescent bulbs is 1400 hours. As a quality control engineer, you need to make sure that the manufacturing process is operating correctly. You randomly select 25 bulbs and find that the sample mean is 1349 hours and the sample standard deviation is 80 hours. Assume probability and box plots show approximate normality and no outliers. Test the claim that the bulb lifetime is statistically different than 1400 hours at a 5% level of significance. What does the conclusion mean for the production process? _11_(8 Points) In the context of the above problem, answer the following: a) What would it mean to make a Type I error? b) What would it mean to make a Type II error?\f