Question

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 = 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 95% confidence level if no pooled value for s
had been available?
Show calculations for part a and b.

Answer 1

Hi,

(A)

This can be done by Z-test (for a) and t-test (for b). Null hypothesis would be that there is no systematic error.

for a we have the value of population standarad deviation so we will use Z-test. formula for Z(calc) is given by:

Z(calc) = (xbar-μ) x SQRT(N)/σ = (30.26-30.15) x SQRT(4)/0.094 = 2.34, Z(table) at 95 % confidence interval is 1.96. since Z(calc)>Z(table), so we can reject null hypothesis and the data indicates the presence of systematic error.

(B)

while systematic error will be in the case t(calc) > t(table). Formula for the test is given here: t(calc) = (xbar-μ) x SQRT(N)/s

t(calc) = (30.26-30.15) x SQRT(4)/0.085 = 2.59

degree of freedom is 4-1 = 3. t(table) at 95 % confidence level at 3 degrees of freedom is 3.18. since t(calc)<t(table), we can retain the null hypothesis and the data does not indicate the presence of any systematic error.

I will be glad to help if you need any other information.