1. Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 50 bulbs was selected, the lifetime of each bulb was collected. Consequently following table is the statistic of the sample data. Variables N Sample mean (X) Sample stdev (SX) Lifetime 50 738.44 38.20 a) Based on given sample statistic (mean and standard deviation), what conclusion would be appropriate for a significance level of 0.05. (Show all hypotheses, test statistic value, p- value, and conclusion in terms of problem context) b) What conclusion would be for a significant level of 0.01? [8 points] [3 points]