SOLUTION: A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without

Question 1087398: A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X1 and X2 as given in the table. Consequently, D = X1 X2.
X1: 21.2, 25.4, 20.9, 27.6, 22.8, 27.3, 23.4
X2: 23.8, 25.6, 22.4, 28.3, 24.5, 28.8, 25.2

What critical value should be used at α = 0.05?
2.447
2.365
1.943
1.895
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

If you have your text book with you, then look up in the back of your book at the T table. Most, if not all, stats books will have reference tables in the appendix or in the chapter somewhere. I can't guarantee it will be there. All books are different.

If you can't find it in your book or you don't have your book with you, then you can use an online resource. I recommend using this table. That is the table I will be using.

We have n = 7 as the sample size. Therefore the degrees of freedom (df) is equal to df = n-1 = 7-1 = 6. Using the table I linked previously, locate the df = 6 row. Highlight everything in that row. Then mark the column that has "one tail = 0.05" up at the top. The intersection of this row and column leads to the value 1.943, which is the critical value.

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