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Question 3 [22 marks] A smartphone's battery life is a key feature that manufacturers advertise whenever they release a new model. Some data were collected on the battery lives for four popular smartphone brands. To prevent any potential bias, the data collectors have labelled the four brands as A, B, C and D. For each brand, a random sample of nine smartphones were selected and the battery life under regular conditions (in hours} was measured for each smartphone. Some sample statistics are displayed in the table below. Assume that smartphone battery life is normally distributed for each brand. The overall sample variance of battery life across all brands was fir453. Brand Sum of Sample Values Sum of Squared Sample Values A 29 314,-: 64. 8 E9: 171;. = 472.34 B E _ Ygi _ 72. 9 24: Y1; = 597.57 C E _ Ym _ 72 9 29:. Ya. = 598.67 D 21:: Ym 31.0 21-11 331. = 735.74 (a) [4 marks] Test whether the population variance of battery life is the same for the brand A and brand C smartphones. Clearly state your hypotheses and use a significance level of a = 1%. (b) [5 marks] Test whether the mean battery life for the brand C smartphone is more than 15 minutes longer than for the brand A smartphone. Clearly state your hy- potheses and use a significance level of a = 10%