Computers in some vehicles calculate various quantities related to performance.

Question

Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the mpg were recorded each time the gas tank was filled, and the computer was then reset. Here are the mpg values for a random sample of 20 of these records: 45.0 50.1 44.0 46.5 41.5 39.4 48.8 52.4 43.4 38.6 49.4 45.3 39.4 45.2 36.4 46.7 46.1 49.8 45.2 48.3

Find the margin of error for 95% confidence. (Round your answer to four decimal places.)

Report the 95% confidence interval for , the mean mpg for this vehicle based on these data. (Round your answers to four decimal places.)

Explanation / Answer

for (n-1=19) degree of freedom and 95% Confidence level ; t=2.093

hence margin of error =t*Std error =2.0040

95% confidence interval for =sample mean -/+ margin of error = 43.0710 ; 47.0790

X 45 50.1 44 46.5 41.5 39.4 48.8 52.4 43.4 38.6 49.4 45.3 39.4 45.2 36.4 46.7 46.1 49.8 45.2 48.3 mean(X) 45.075 std deviation(S) 4.2819 std error =S/(n)1/2 0.9575

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