Question 1157102: 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.
...........City MPG, Automatic......City MPG, Manual
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Mean....|..16.12..................|...19.85
SD......|..3.58...................|...4.51
n.......|...26....................|...26
The hypotheses for this test are:
Ho: μautomatic = μmanual
Ha: μautomatic < μmanual
Ho: μautomatic = μmanual
Ha: μautomatic ≠ μmanual
Ho: μautomatic = μmanual
Ha: μautomatic > μmanual
The test statistic is: _______ (please round to two decimal places)
The p-value is: _______ (please round to four decimal places)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The wording is "strong evidence of a difference" without specifying which direction. This is therefore a two way test, so the pair is = or not =.
That makes the third and fourth the hypotheses of choice.
Test stat is -3.30
p=0.0018
Normally, I require the hypotheses together to encompass everything, but this belief is not universally agreed upon. But when Ho is equal, Ha must be NOT EQUAL.
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