Are the tablets over their 500 mg target dose?

Question

A pharmaceutical line is supposed to press tablets containing 500 mg of active ingredient. A quality analyst assays 8 tablets and finds a mean of 506 mg with a sample standard deviation of 6 mg. The population standard deviation is unknown.

Test at the 5% level (two-sided) whether the true mean dose differs from 500 mg, and report the t-statistic.

Accepted Answer

Unknown \sigma with a small sample, so use a one-sample t-test with 8 - 1 = 7 degrees of freedom. Hypotheses: H0: \mu = 500 versus H1: \mu 
eq 500. Standard error: 	ext{SE} = \frac{6}{\sqrt{8}} = \frac{6}{2.828} = 2.121 	ext{ mg}. Test statistic: t = \frac{506 - 500}{2.121} = \frac{6}{2.121} = 2.83. The two-sided 5% critical value for 7 degrees of freedom is t{0.025,\,7} = 2.365. Since 2.83 2.365, reject H0. The two-sided p-value is about 0.025. Conclusion: there is evidence the tablets are running above the 500 mg target, a real concern for dosing. Takeaway. With only 8 observations the t…

Are the tablets over their 500 mg target dose?

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