Question

A sample of 8 new models of automobiles provides the following data on highway miles per gallon. Highway Miles Model Per Gallon 1 33.6 2 26.8 3 20.2 4 38.7 5 35.1 6 28.0 7 26.2 8 27.6 a. What is the point estimate for the average highway miles per gallon for all new models of autos? b. Determine the point estimate for the standard deviation of the population.

Answer 1

The point estimate for the mean is 29.5 miles per gallon and the standard deviation is 5.9

Explanation:

The formula por the point estimate of the mean is:

`mean(x) = (x1+x2+x3+...+xn)/(n)`

And for the standard deviation:

`desv(x)=((1)/(n-1)sum(xi^(2) - n*x^(2) ))^(1/2)`

So for the mean:

`mean(x)=(33.6+26.8+20.2+38.7+35.1+28.0+26.2+27.6 )/(8) \\\\mean(x)=(236.2)/(8) \\\\mean(x)=29.5`

And for the standard deviation:

`desv(x)=((1)/(8-1) ((33.6-29.5)^(2) +(26.8-29.5)^(2) +(20.2-29.5)^(2) +(38.7-29.5)^(2) +(35.1-29.5)^(2) +(28-29.5)^(2) +(26.2-29.5)^(2) +(27.6-29.5)^(2))^(1/2) \\\\desv(x)=((1)/(8-1) ((4.1)^(2) +(-2.7)^(2) +(-9.3)^(2) +(9.2)^(2) +(5.6)^(2) +(-1.5)^(2) +(-3.3)^(2) +(-1.9)^(2))^(1/2) \\\\desv(x)=\sqrt{(243.3)/(7)} \\\\desv(x)=√(34.7) \\\\desv(x)=5.9`