Question 10 A random sample of 10 Xcars achieved the followi

Question 10 A random sample of 10 X-cars achieved the following fuel consumption figures, in miles per gallon: 27.2 27.2 26.8 26.9 25.3 26.0 26.4 25.7 28.1 25.7 An independent random sample of 12 Y-cars achieved the following results: 24.2 24.3 25.3 24.8 25.1 25.0 24.9 23.9 26.0 26.1 26.0 26.3 Use an unbiased estimation procedure to obtain a point estimate of the difference in population mean fuel consumption between X-cars and Y-cars. Use an unbiased estimation procedure to obtain a point estimate of the difference between the population proportion of X-cars achieving more than 25.5 miles per gallon and the population proportion of Y-cars achieving more than 25.5 miles per gallon 12

Solution

The sample mean for X cars is 26.53

The sample mean for Y cars is 25.15833

So an unbiased estimation = 26.53-25.15833 =1.37167

-------------------------------------------------------------------------------------------------------

There are 9 x-cars achieve more than 25.5 miles per gallon

So the proportion is 9/10=0.9

There are 4 y-cars achieve more than 25.5 miles per gallon

So the proportion is 4/12=0.3333

So an unbiased estimation =0.9-0.3333 =0.5667