Question

You purchase a standard reference material iron sample that is certified by the national institute of standards and technology to contain 1.33 wt% Fe. you want to test a new analytical method to see if it can reproduce the known value within the 95% confidence interval. the measured values are 1.56, 1.45, 1.39, 1.29, and 1.46 wt% Fe (mean = 1.43% wt% Fe and stdev = 0.0993 wt% Fe). Does your new analytical method reproduce the known value within the 95% confidence interval? Explain.

Answer 1

We will calculate the confidence interval as

= $CI = \bar{x} \pm \frac{ts}{\sqrt{n}}$

Where

x = average = 1.43

s = standard deviation = 0.0993

n = sample size = 5

t= student's t- test (obtained from statitstical table), obtaned fir 4 degree of freedon and 95% inteval = 2.776

CI = 1.43 +/- 2.776 X 0.0993 / (5)^1/2 = 1.43 +/- 0.123

the experimental value obtained = 1.33 , which is within the 95% confidence interval