You are checking the accuracy of a volumetric flask marked 10.00 mL Measurement

Question

You are checking the accuracy of a volumetric flask marked 10.00 mL Measurement Volume (mL) You measure the volume of water contained in the flask by measuring the mass of the empty flask, the mass of the flask filled with water taking the difference, correcting for the buoyancy factor, and dividing by the density of the water. The result of eight such measurements is given in the table at the right. 10.051 10.061 10.023 10.059 10.023 10.012 10.050 2 4 Calculate the mean and the 95% confidence interval for these measurements mean 7 10.006 Note: Be sure not to round your answers until the very end of your calculations Number Number Can you, with 95% confidence, say that the nominal value of 10.00 mL can be the true volume of the flask? Yes O No

Explanation / Answer

Initially we calculate the average of the samples:

X = (Sum Xi) / n = 80,285 / 8 = 10,036 mL

Next we calculate the standard deviation:

SD = [Sum (Xi-X) 2] / [n-1] = 0.02

Finally we calculate the value of the confidence limit:

Z (0.025) * SD / n = 1.96 * 0.02 / 8 = 0.014

Then we express the confidence interval at 95%:

10,036 ± 0.014

[10,022; 10,050]

we can not accept the value of V = 10 mL because it is not within the confidence interval.

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