Fuel efficiency of manual and automatic cars, Part I: Each year the US Environme

Question

Fuel efficiency of manual and automatic cars, Part I: Each year the US Environmental 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 manual and automatic transmissions in terms of their average CITY mileage? Assume that conditions for inference are satisfied. USE YOUR TI CALCULATOR. Use a significance level of 1%. You are estimating meu _automatic - meu_manual The test statistic is (please round to two decimal places) The p-value is: (please round to four decimal places) Interpret the result of the hypothesis test in the context of the problem: The data provide sufficient evidence that there is a difference between the average fuel efficiency of manual and automatic cars in terms of their average city mileage The data do not provide sufficient evidence that there is a difference between the average fuel efficiency of manual and automatic cars in terms of their average city mileage The data provide sufficient evidence that there is no difference between the average fuel efficiency of manual and automatic cars in terms of their average city mileage.

Explanation / Answer

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 = u2
Alternate Hypothesis, There Is Significance between them - H1: u1 != u2
Test Statistic
X(Mean)=16.12
Standard Deviation(s.d1)=3.58 ; Number(n1)=26
Y(Mean)=19.85
Standard Deviation(s.d2)=4.51; Number(n2)=26
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =16.12-19.85/Sqrt((12.8164/26)+(20.3401/26))
to =-3.303
| to | =3.303
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 25 d.f is 2.787
We got |to| = 3.30302 & | t | = 2.787
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -3.303 ) = 0.003
Hence Value of P0.01 > 0.003,Here we Reject Ho

[ANSWERS]
a. Ho: u1 = u2 , H1: u1 != u2
b. The data provide sufficient evidence that there is a difference between the average fuel efficiency of manual and
automatic cars in terms of their average city mileage

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