Each year the US Environ-mental Protection Agency (EPA) releases fuel economy da

Question

Each year the US Environ-mental Protection Agency (EPA) releases fuel economy data on cars manufactured in that year. Below are summary statistics on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions manufactured in 2012. Do these data provide strong evidence of a difference between the average fuel efficiency of cars with a manual and automatic transmissions in terms of their average city mileage? Conduct a hypothesis test AND construct a confidence interval to support your answer. Assume that conditions for inference are satisfied.

Explanation / Answer

M1-M2=16.12-19.85=-3.73

since n1= n2

s_p = sqrt((s1^2 +s2^2/)2) =sqrt((3.58^2+4.51^2)/2) = 4.0176

test-statistics =

(16.12-19.85)/(4.0176*sqrt(2/26))

= -3.34

degree of freedon = 26+26-2 = 50

t-ctitical = 2.009

since |TS| > t-ctitical

we reject the null

and conclude that there is difference between the average fuel efficiency of cars with a manual and automatic transmissions in terms of their average city mileage

confidence interval

(-3.73 -2.009*4.0176*sqrt(2/26)),(-3.73 +2.009*4.0176*sqrt(2/26))

=(-5.9685,-1.491407)

since each value is less than 0 , CI support our results

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