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

Question

5.32 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.

5.32 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 (irn 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. City MPG, Automatic City MPG, Manual 19.85 4.51 26 16.12 3.58 26 Mean SD 35 1 25 15 automatic manual City MPG

Explanation / Answer

The statistical software output for this problem is:

Two sample T summary hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 0
(without pooled variances)

Hypothesis test results:

Hence,

Hypothesis: Option B is correct.

Test statistic = -3.30

P - value = 0.0018

Conclusion: Option A is correct.

Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 -3.73 1.1292697 47.551555 -3.3030197 0.0018

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