# hypothesis test

Ten automobiles were driven on a measured test track - once with standard gasoline with no additive and once with an additive supposed to increase miles per gallon (mpg). The results are given below:

mpg / car # 1 2 3 4 5 6 7 8 9 10

without additive 19 22 25 18 26 21 23 28 24 24

with additive 22 24 26 21 27 24 26 32 23 27

Test the null hypothesis that the additive has no or negative effect against the alternative hypothesis that it has a positive effect on mileage at the alpha = 0.05 level of significance.

My initial thoughts are:

Ho: mean(w/o additive) >= mean (w /additive)

Ha: mean(w/o additive) < mean (w/additive)

So this appears to be a one-tailed t-statistic with 2 population means, is this right? How would this problem work? Formulas appreciated.

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#### Solution Summary

It provides examples of working with hypothesis testing. The effects on mileage at the alpha with a significance level is determined. Alternative hypothesis are analyzed.