Challenge Problem: The following are three sets of data for the atomic mass of antimony from the work of Willard and McAlpine7:
Set 1 | Set 2 | Set 3 |
121.771 | 121.784 | 121.752 |
121.787 | 121.758 | 121.784 |
121.803 | 121.765 | 121.765 |
121.781 | 121.794 |
(a) Determine the mean and the standard deviation for each data set.
(b) Determine the 95% confidence interval for each data set.
(c) Determine whether the 121.803 value in the first data set is an outlier for that set at the 95% confidence level.
(d) Use the t test to determine whether the mean of data set 3 is identical to that of data set 1 at the 95% confidence level.
(e) The means of all three data sets are to be compared by ANOVA. State the null hypothesis. Determine whether the means differ at the 95% confidence level.
(f) Pool the data and determine the overall mean and the pooled standard deviation.
(g) Compare the overall mean of the 11 data points to the currently accepted value. Report the absolute error and the relative error in percent assuming the currently accepted value is the true value.
7H. H. Willard and R. K. McAlpine, J. Am. Chem. Soc., 1921, 43, 797, DOI: 10.1021/ja01437a010.
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