Working for a car company, you have been assigned to nd the average miles per ga

ID: 3174632 • Letter: W

Question

Working for a car company, you have been assigned to nd the average miles per gallon (mpg) for a certain

model of car. You take a random sample of 15 cars of the assigned model. Based on previous evidence and

a QQ plot, you have reason to believe that the gas milage is normally distributed. You nd that the sample

average miles per gallon is around 26:7 with a standard deviation of 6:2 mpg.

(a) Construct and interpret a 95% condence interval for the mean mpg, , for the certain model of car.

(b) What would happen to the interval if you increased the condence level from 95% to 99%? Explain

your reasoning. (Do not compute the new interval.)

the whole interval to be less than 4 mpg wide. How many cars would you have to sample to create the

interval the engineer is requesting?

(d) Suppose you are asked to repeat this process with data gathered from all across the country. You end

up constructing a total of 60 separate 95% condence intervals at dierent factories for the estimated

average mpg of the model of car. Of these intervals, how many of them do you expect would fail to

contain the true value of ?

a) std error of the mean =std deviaiton/(n)1/2 =1.6008

for 14 degree of freedom and 95% CI ; t=2.1448

hence confidence interval =sample mean +/- t*std error =23.267 ; 30.133

b)as confidence interval increases, width will increase as the value of t does increases

c)here for 95% CI; z=1.96

and margin of error E =4/2 =2

hence sample size n=(z*std deviation/E)2 ~37

d) total number of values=np=60*0.95=57

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