Question

It is known from many careful measurements that the concentration of magnesium in a material is 0.217 wt%. Your new analytical procedure gives values of: 0.218, 0.220, 0.219, 0.217, 0.215, 0.221 wt%. Do your results systematically differ from the expected result at 95% confidence level?

Answer 1

H0: Null Hypothesis: = 0.217

HA: Alternative Hypothesis: 0.217

From the given data, the following statistics are calculated:

n = Sample size = 6

= Sample Mean = 1.31/6 = 0.2183

s =Sample SD =0.0022

SE = s/

= 0.0022/ = 0.0008981

Test statistic is:

t = (0.2183 - 0.217)/0.0008981= 1.45

= 0.05

ndf = n - 1 = 6- 1 = 5

From Table, critical values of t = 2.5706

Since the calculated value of t = 1.45 is less than critical value of t = 2.5706, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that your results systematically differ from the expected result.