An e in the November 19B3 Consumer Reports compared various types of batteries.

Question

An e in the November 19B3 Consumer Reports compared various types of batteries. The average lifetimes of Duracell Alkaline AA batteries and Eveready EnergizerAlkne AA batteries were given as 4.1 hours and 4.5 hours, respectively. Suppose these are the population average lifetimes. (a) Let X be the sample average lifetime of 144 Duracell and ? be the sample average lifetime of 144 Eveready Energizer batteries. what is the mean value of X-Y (i.e., where is the distribution of X-Y centered)? Does your answer depend on the specified sample sizes? The answer decreases as the sample size decreases. The answer decreases as the sample size increases. The answer increases as the sample size decreases. The answer increases as the sample size increases. The answer is the same irrespective of the sample sizes. b) Suppose the population standard deviations of lifetime are 1.5 hours for Duracell batteries and 3.0 hours for Eveready Energizer batteries. with the sample sizes given in part (a), what is the variance of the statistic ?-Y, and what is its standard deviation? (Round your answers to four decimal places.) varance standard deviation (c) For the sample sizes given in part (a), draw a picture of the approximate distribution curve of X - Y (include a measurement scale on the horizontal axis) 0.5 0.0 0.5 1.0-0.8-0.6-0.4-0.2 0.0 0.2 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 -0.5 0.0 0.5

Explanation / Answer

a)

mean value of Xbar-Ybar=4.1-4.5 =-0.4

the answer is the same irrespective of sample sizes

b)

varaince =(1.52/144+32/144)=0.0781

std deviation=0.2795

c)

first curve is right

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