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(BENG 2143) QUESTION 2 A factory wants to investigate if the mean lifetimes of the four brands of batteries they produced are the same. The factory's research department randomly selected a few batteries of each brand and tested them. Table Q2(a) lists the number of hours (in thousands) that each of the battery in each brand lasted before being burned out: Table Q2(a): The number of hours (in thousands) that each of the battery in each brand lasted before being burned out Brand A Brand B Brand C Brand D 23 19 23 26 24 23 28 24 29 14 25 21 16 24 26 30 22 15 23 28 23 22 21 24 25 X 27 28 (a) Construct an ANOVA table consisting of the source of variances, sum of squares, mean squares and F value for the mean lifetimes of the four brands of batteries if y.. = 23.25 (you will first need to determine the value of x). Perform the analysis of variance at the 5% level of significance. What can you conclude based on the F value at the 5% significance level? [21 marks] (b) If the significance level is decreased to 0.1%, will it affect your conclusion in 2(a)? Show your solution in detail. [4 marks]