Dylan Jones kept careful records of the fuel efficiency of his new car. After th

Question

Dylan Jones kept careful records of the fuel efficiency of his new car. After the first eight times he filled up the tank, he found the mean was 21 miles per gallon (mpg) with a sample standard deviation of 1.1 mpg. (Use  t Distribution Table.)

Compute the 99% confidence interval for his mpg. (Round your answers to 3 decimal places.)

To be 99% confident, how many times should he fill his gas tank to obtain a margin of error below 0.2 mpg? (Round up your answer to the next whole number.)

Dylan Jones kept careful records of the fuel efficiency of his new car. After the first eight times he filled up the tank, he found the mean was 21 miles per gallon (mpg) with a sample standard deviation of 1.1 mpg. (Use  t Distribution Table.)

Explanation / Answer

a) std error of mean =std deviation/(n)1/2 =1.1/(8)1/2 =0.3889

here for 99% level and (n-1=7) degree of freedom ; t=3.4995

therefore 99% confidence interval =sample mean -/+ t*std error =19.639 ; 22.361

b) here margin of error E =0.2

for 99% CI, z=2.5758

hence sample size n=(z*std deviation/E)2 =201

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