The National Institute of Standards and Technology (NIST) offers a wide variety of “standard reference materials” (SRMs) with accurately specified analyte concentrations. SRM 1951c is intended in part for “evaluating the accuracy of clinical procedures for the determination of total cholesterol . . . in human serum.” The certified total cholesterol is 6.244 ± 0.072 mmol/L. For the sake of this question, let’s treat 6.244 mmol/L as its “true” value (μ). We will use this standard to test a method with an intrinsic variability (for an experienced analyst) of σ = 0.131 mmol/L. In three trials, you obtained the following cholesterol concentrations (all in mmol/L): 6.476, 6.590, 6.338. 1. Showing all work, calculate a 95% confidence interval for your measured cholesterol concentration and write it as an intermediate result (with guard digits). Does your measurement differ from μ at 95% confidence? 2. Repeat part 1 for 90% confidence and explain any change in your conclusion. 3. Another student performed the same analysis and in 4 trials measured a mean of 6.176 mmol/L and a standard deviation of 0.188 mmol/L. Does this measurement differ from yours at 95% confidence? Show all work, including the value of t-table you used. [Assume that the standard deviations are not “significantly different.”]
The National Institute of Standards and Technology (NIST) offers a wide variety of “standard reference materials” (SRMs) with accurately specified analyte concentrations. SRM 1951c is intended in part for “evaluating the accuracy of clinical procedures for the determination of total cholesterol . . . in human serum.” The certified total cholesterol is 6.244 ± 0.072 mmol/L. For the sake of this question, let’s treat 6.244 mmol/L as its “true” value (μ). We will use this standard to test a method with an intrinsic variability (for an experienced analyst) of σ = 0.131 mmol/L. In three trials, you obtained the following cholesterol concentrations (all in mmol/L): 6.476, 6.590, 6.338.
1. Showing all work, calculate a 95% confidence interval for your measured cholesterol concentration and write it as an intermediate result (with guard digits). Does your measurement differ from μ at 95% confidence?
2. Repeat part 1 for 90% confidence and explain any change in your conclusion.
3. Another student performed the same analysis and in 4 trials measured a mean of 6.176 mmol/L and a standard deviation of 0.188 mmol/L. Does this measurement differ from yours at 95% confidence? Show all work, including the value of t-table you used. [Assume that the standard deviations are not “significantly different.”]
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