(*explaining how to do this, step by step; while how to compute this with a TI-8
ID: 3330815 • Letter: #
Question
(*explaining how to do this, step by step; while how to compute this with a TI-84, if possible/ applicable please)
You are in the market for a new car. You want to check whether there is a significant difference between the fuel economy of mid-size domestic cars and mid-size import cars. You sample 18 domestic car makes and find an average fuel economy of 30.493 MPG with a standard deviation of 5.456 MPG. For imports, you sample 11 cars and find an average MPG of 34.197 MPG with a standard deviation of 7.542. If a 99% confidence interval is calculated to estimate the difference between the average fuel economy of domestic and import mid-size cars, what is the margin of error? Assume both population standard deviations are equal.
Question 9 options:
1)
2.771
2)
5.971
3)
6.221
4)
2.415
5)
6.692
1)
2.771
2)
5.971
3)
6.221
4)
2.415
5)
6.692
Explanation / Answer
Data given for domestic cars:
Sample mean, m1 = 30.493
Sample size, n1 = 18
Sample SD, S1 = 5.456
Data given for imports:
Sample mean, m2 = 34.197
Sample size, n2 = 11
Sample SD, S2 = 7.542
Calculating standard error:
SE = (S12/n1 + S22/n2)0.5 = (5.4562/18 + 7.5422/11)0.5 = 2.612
For 99% CI, the margin of error is:
ME = 2.58*SE = 2.58*2.612 = 6.73
So, the correct answer is 6.692
Hope this helps !
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