LasiFirst roblsuracell Alkaline AA batteries and Eveready Energizer Alkaline A b
ID: 3321593 • Letter: L
Question
LasiFirst roblsuracell Alkaline AA batteries and Eveready Energizer Alkaline A batietease or 4 5 hours and 4.2 hours, respectively. Suppose these are the -A study comparing different types of batteries showed that the average Date: were given population average lifetimes Let be the sample average lifetime of 150 Duracell batteries average lifetime of 150 Eveready batteries. What is the meanv where is the distribution of X -9 centered)? and ? be the sample aluc of X Y (i.e.. How does your answer in part (a) depend on the specified sample sizes? b. c. Suppose the population standard deviations of lifetime are 1.8 hours for Duracell batteries and 2.0 hours for Eveready batteries. With the sample sizes given in part (a), what is the variance of the statistic X 9, and what is its standard deviation? d. For the sample sizes given in part (a), what is the approximate distribution curve of X - Y? Would the shape of the curve necessarily be the same for sample sizes of 10 batterie of each type? Explain. e.Explanation / Answer
a)Mean: E(Xbar - Ybar) = E(Xbar) - E(Ybar) = 4.5-4.2 = 0.3 hours
b) NO, it does not depends on the specified sample sizes
c) Var(Xbar - Ybar) = Var(Xbar) + Var(Ybar) = (1.8^2)/150 + (2^2)/150 = 0.048267
SD(Xbar - Ybar) = Sqrt(0.048267) = 0.219697
d) Normal distribution
e) Bell shaped curve
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