The built-in data set \"mtcars\" compares 11 aspects of automobile design for 32

Question

The built-in data set "mtcars" compares 11 aspects of automobile design for 32 different 1974 model automobiles. We will be looking at the wt column of mtcars. Assume that the 32 cars are a random sample of all 1974 automobiles. We would like to estimate the true mean value, , of the wt (weight in 1000's of pounds) of cars in 1974. The unknown variance of wt is 2. Using R define the vector x by x<-mtcars$wt. A screen print of the data follows.

[1] 2.620 2.875 2.320 3.215 3.440 3.460 3.570 3.190 3.150 3.440 3.440 4.070 3.730

[14] 3.780 5.250 5.424 5.345 2.200 1.615 1.835 2.465 3.520 3.435 3.840 3.845 1.935

[27] 2.140 1.513 3.170 2.770 3.570 2.780

c) Assuming normality of car weights, calculate is the maximum likelihood estimate of 2.

d) Calculate an unbiased point estimate of the population variance, 2 of cars in 1974.

e) Assuming normality of car weights, calculate the maximum likelihood estimate of  ?  

f) Calculate the 65th percentile of x using R.  

Explanation / Answer

#C
#MLE
m1=sum((x-mean(x))^2)/length(x)
#Mle is 0.9274609
#d
#Unbiased Point estimate
mun=sum((x-mean(x))^2)/(length(x)-1)
#Unbiased estimate of the variance is .957379

e) mean(x)
[1] 3.21725

f) quantile(x,0.65)
65%
3.469
>

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