A tritrimetric method for the determination of calcium in limestone was tested b
ID: 736315 • Letter: A
Question
A tritrimetric method for the determination of calcium in limestone was tested by analysis of a NIST limestone containing 30.15% CaO. The mean result of four analyses was 30.26% CaO, with a standard deviation of 0.085%. By pooling data from several analyses, it was established that s --> sigma = 0.094% CaO.a.) Do the data indicate the presence of a systematic error at the 95% confidence level?
b.) Would the data indicate the presence of a systematic error at the 95% confidence level if no pooled value for s had been available?
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Explanation / Answer
The practice of science involves formulating and testing hypotheses, assertions that are capable of being proven false using a test of observed data. The null hypothesis typically corresponds to a general or default position. For example, the null hypothesis might be that there is no relationship between two measured phenomena[1] or that a potential treatment has no effect.[2] The term was originally coined by English geneticist and statistician Ronald Fisher in 1935.[3][4] It is typically paired with a second hypothesis, the alternative hypothesis, which asserts a particular relationship between the phenomena. Jerzy Neyman and Egon Pearson formalized the notion of the alternative. The alternative need not be the logical negation of the null hypothesis; it predicts the results from the experiment if the alternative hypothesis is true. The use of alternative hypotheses was not part of Fisher's formulation, but became standard. It is important to understand that the null hypothesis can never be proven. A set of data can only reject a null hypothesis or fail to reject it. For example, if comparison of two groups (e.g.: treatment, no treatment) reveals no statistically significant difference between the two, it does not mean that there is no difference in reality. It only means that there is not enough evidence to reject the null hypothesis (in other words, the experiment fails to reject the null hypothesis)
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