Question

A laboratory manager wants to ensure that 95% of the carbon analysis measurements made in the laboratory are within 0.1 ppm of the true value. On the basis of experience, the manager is willing to assume that the carbon content measurements made on identical soil samples are approximately normally distributed with mean µ and standard deviation ? . Recall that 95% of the measurements in a normal population lie within 1.96 (about 2) standard deviations of the mean. The requirement will be met if 2 0.10 or 0.05 ?? ?? . Based on the ten data values below (ppm) use the chi-square test for a single variance to see if the measurement precision can be met with the instrumentation being used. Recall the chi-square test is set up for the variance, not the standard deviation. Use a Type I error of 0.05.

0.560 0.842 0.731 0.782 0.673 0.718 0.791 0.726 0.760 0.798

Answer 1

= 0.738, s^2 = 0.0062

H₀: = 0.01

H₁: 0.01

The test statistic = (n - 1)s^2/

                                = 9 * 0.0062/0.01 = 5.58

At alpha = 0.05, the critical values arre = 2.7004

                                                               = 19.0228

AS the test statistic value lies between the critical values (2.7004 < 5.58 < 19.0228), so the null hypothesis is not rejected.

So at alpha = 0.05, we can conclude that the measurement percision can be met with the instrumentation being used.