An article in the november 1983 consumer reports compared various types of batteries. the average life-times of duracell alkaline aa batteries and eveready energizer alkalineaa batteries were given as 4.1 hours and 4.5 hours, respectively. suppose these are thepopulation average lifetimes. a.let¯xbe the sample average lifetime of 100 duracell batteries and¯ybe the sampleaverage lifetime of 100 eveready batteries. what is the mean value of¯x-¯y(i. e.,where is the distribution of¯x-¯ycentered)? how does your answer depend on thespecified sample sizes? e(¯x-¯y) =e(¯x)-e(¯y) =μ¯x-μ¯y=μx-μy= 4.1-4.5 =-0.4the mean value of¯x-¯ydoes not depend on the sample size. b.suppose the population standard deviations of lifetime are 1.8 hours for duracellbatteries and 2.0 hours for eveready batteries. with the sample sizes given in part(a), what is the variance of the statistic¯x-¯yand what is the standard deviation? v(¯x-¯y)=v(¯x) +v(¯y) =σ2¯x-σ2¯y=σ2x/√m-σ2y/√n=(1.8)2/100 + 22/100 =0.0724qv(¯x-¯y)=0.2691