Instrumental methods of analyses class? A titrimetric method for the determinati

Question

Instrumental methods of analyses class?

A titrimetric method for the determination of calcium in limestone was tested by analysis of a NIST containing 30.15% Cao. The mean result of four analyses was 30.26% Cao, with standard deviation of 0.085%. By pooling data from several analyses, it was found that s o 0.094% CaO. Do the data indicate the presence of a systematic error at the 95% confidence level? Would the data indicate the presence of a systematic error at 95% confidence level if no pooled value for s had been available? Show calculations for part a and b.

Explanation / Answer

Solution

Part (a)

We need to test H0: µ = 30.15% vs HA: µ 30.15%

Test statistics for this test is: t = {(n)(x bar - µ)/s}, where n = sample size (= 4), x bar is the sample average, µ = 30.15% and s (= 0.094) is the pooled estimate of the population standard deviation, .

So, t = 2(30.26 – 30.15)/0.094 = 0.22/0.094 = 2.340.

Decision Criterion: Reject H0 , if calculated value of t is greater than the upper % point of t-distribution with (n - 1) degrees of freedom. Given = 5(because of 95% confidence), the upper point of t3 = 3.182. Since 2.340 < 3.182, H0 is accepted implying that there is no indication of systematic error.

Part (b)

If the estimate of in the form of pooled value of s were not available, we would have used the obtained sample variance (0.085) in its place and value of t would have been 2.589 which is still less than 3.182. Hence, the decision remains unaltered.

(d) A process D that is neither a Martingale nor a Markov process.

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