Measuring Weights? When certain quantities are measured, the last digits tend to be uniformly distributed, but if they are estimated or reported, the last digits tend to have disproportionately more 0s or 5s. If we use the last digits (decimal portion) of the 80 weights in Data Set 1 from Appendix B, we get the frequency counts in the table below. Use a 0.05 significance level to test the claim that the last digits of 0, 1, 2, . . . , 9 occur with the same frequency. Does it appear that the weights were obtained through measurements? L a s t D i g i t F r e q u e n c y

Solution 2RE Step1: Consider the hypothesis H : Last digits occur with the same probability. 0 H : Last digits do not occur with the same probability. 1 Level of significance, . The observed and expected frequencies are shown in the below table. (O - E)² / observed expected O - E E 6 8.000 -2.000 0.500 7 8.000 -1.000 0.125 4 8.000 -4.000 2.000 11 8.000 3.000 1.125 10 8.000 2.000 0.500 8 8.000 0.000 0.000 5 8.000 -3.000 1.125 9 8.000 1.000 0.125 10 8.000 2.000 0.500 10 8.000 2.000 0.500 =6.500 Here, we have p value is p = 0.689 And from the above given data set = 6.500 since the p value is less than the hence, Hence we fail to reject the null hypothesis that last digits of occur with the same frequency. It also appears that the weights were obtained through measurements.