2. A quality control engineer finds that a sample of 100 light bulbs had an average life time of 470 hours. Assuming a population mean of 480 hours with standard deviation of g = 25 hours. Test whether data indicates the mean life time of bulbs is less than 480 hours at 5% level of significance. a). Write down all the details given in the problem [2 points]
b). State the hypotheses [6 points]
c). Find the critical value and draw in on a bell curve [2 points]
d). Calculate the test statistic [5 points]
e). Find p-value [4 points]
f). What is your decision? [2 points]
g). Interpret your decision in context of the problem. [4 points]