It is known from many careful measurements that the concentration of magnesium i

Question

It is known from many careful measurements that the concentration of magnesium in a material is 0.135 wt %. Your new analytical procedure gives values of 0.129, 0.131, 0.136, 0.130, 0.128 and 0.127 wt %. Calculate the mean and standard deviation of the experimental data and determine whether a positive error is indicated at the 90% confidence level. Determine whether the value 0.136 should be rejected from the set of results. (t = 2.353 for three degrees of freedom and t = 2.132 for four degrees of freedom, and values for Q at 90% confidence: n = 3 0.94; n = 4 0.76; n = 5 0.64 )(20 points)

Explanation / Answer

Mean deviation = (0.129 + 0.131 + 0.136 + 0.130 + 0.128 + 0.127)/6 = 0.1302

Standard deviation:

0.129-0.1302 = -0.0012 = 1.44 x 10^-6

0.131-0.1302 = 0.0008 = 6.4 x 10^-7

0.136-0.1302 = 0.0058 = 3.364 x 10^-5

0.130-0.1302 = -0.0002 = 4 x 10^-8

0.128-0.1302 = -0.0022 = 4.84 x 10^-6

0.127-0.1302 = -0.0032 = 1.024 x 10^-5

variance = 1.0168 x 10^-5

standard deviation = 0.0032

The value 0.136 is far off and should be thus rejected from the set of data.

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