A chemis is interested in the amount of impurities in a liquid that she could pr

Question

A chemis is interested in the amount of impurities in a liquid that she could produce by a chemical process. he was concerned that the liquid would not be satisfactory for use if tghe impurity level went above 12. To Test her process of making the liquid, she made 9 samples of the liquid and found the sample impurities had an average of 17 with a SD of 6. Carry out a test of the hypotheses H: mean is less than or equal to 12 vs. Ha :mean is greater than 12 where the mean is the average impurity level for her process.

Explanation / Answer

Let us take the confidence level to be 95%

SE = SD/square root(n) = 6/3 = 2

Since population standard deviation is unknown,

therefore we will use t distribution for hypothesis testing

Crtical t = 1.860 {t distribution with degree of freedom 8, one tail test with alpha=0.05}

test statistic = (17-12)/2 = 5/2 = 2.5

Since test statistic > Critical t, thus reject the Null hypothesis.

Mean is indeed greater than 12 with 95% confidence.

Although, with 99% level it is opposite because critical t is 2.896

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