The Environmental Protection Agency (EPA) conducted an experiment to determine the effect of adding ethanol to gasoline. First 40 automobiles had their gas tanks completely drained and then filled with exactly 15 gallons of gasoline without ethanol. Then these auto were driven on a closed course for 200 miles. Next their gas tanks were drained and the amount of gasoline used by each auto was thus determined. The second phase of the experiment was to fill these same automobiles with 15 gallons of gasoline with ethanol, drive them on the same closed course for 200 miles, and then drain their gas tanks to determine the amount of fuel used by each auto. The differences between the gasoline without and with ethanol were computed for each automobile, and the EPA computed the mean of these differences as 0.31 gallons and a standard deviation of 0.74. Let? = 0.01, and test to see if there is a significant difference in the mean number of gallons used between the two types of gasoline.

Question

Mathematics

Phillip Barker

5 June, 14:18

The Environmental Protection Agency (EPA) conducted an experiment to determine the effect of adding ethanol to gasoline. First 40 automobiles had their gas tanks completely drained and then filled with exactly 15 gallons of gasoline without ethanol. Then these auto were driven on a closed course for 200 miles. Next their gas tanks were drained and the amount of gasoline used by each auto was thus determined. The second phase of the experiment was to fill these same automobiles with 15 gallons of gasoline with ethanol, drive them on the same closed course for 200 miles, and then drain their gas tanks to determine the amount of fuel used by each auto. The differences between the gasoline without and with ethanol were computed for each automobile, and the EPA computed the mean of these differences as 0.31 gallons and a standard deviation of 0.74. Let? = 0.01, and test to see if there is a significant difference in the mean number of gallons used between the two types of gasoline.

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Glover · Answer 1

Step-by-step explanation:

I used the paired sample t test as the same population of 40 cars is being tested.

The Hypothesis:

H0: = 0

Ha: 0

The Test statistic:

The p value (2 tail) at t = 2.65, df = n - 1 = 40 - 1 = 39 is 0.0116

The Critical value at = 0.01, df = 39 is 2.7079

The Decision Rule: If t observed > 2.7079, Reject H0.

Also if p value is < (0.01), Then Reject H0.

The Decision: Since t observed < 2.7079, Fail to reject H0.

Also Since p value (0.0116) > 0.01, We Fail to Reject H0.

The Conclusion: Fail To Reject H0. There is insufficient evidence at the 99% significance level to conclude that there is a significant difference in the mean number of gallons used between the 2 types of gasoline.