SOLUTION: A chemist compare the sugar contents of two brands of beverages with the same bottle sizes. Ten bottles of Brand X had an average sugar content of 3.1 grams with a standard deviat

Question 1160297: A chemist compare the sugar contents of two brands of beverages with the same bottle sizes. Ten bottles of Brand X had an average sugar content of 3.1 grams with a standard deviation of 0.5 grams, while eight bottles of Brand Y had an average sugar of 2.7 grams with a standard deviation of 0.7 grams. We know that two sets of data are independent random samples from normal populations, and they have equal variances. Construct a 95% confidence interval for the difference (X-Y) between the mean sugar contents of the two brands of beverages. Decide which brand has a higher sugar ratio.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
the 95% CI (t) is (-0.2382, 1.0382) gms sugar.
Because 0 is in the interval, one cannot conclude that one brand has more sugar than the other.
This can also be done with a two sample t-test with Ho: mu x=mu Y and Ha: mu X ne mu Y
Done with a 2-sample t-test, df=12.3, the test statistic is t=1.36 and the p-value 0.20. This fails to reject the Ho so there is insufficient evidence with these samples to show a difference in sugar ratio.
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