The mean length of a candy bar is supposed to be 43 millimeters. there is 3) concern that the settings of the machine cutting the bars have changed. test the claim at the .02 level that there has been no change in mean length. the alternate hypothesis is that there has been a change. twelve bars (n = 12) were selected at random and their lengths in millimeters are: 42, 39, 42, 45, 43, 40, 39, 41, 40, 42, 43, and 42. the mean length of the sample is 41.5. the sample standard deviation is 1.784. the population standard deviation is not known. if the computed t = −2.913, has there been a statistically significant change in the mean length of the candy bars?

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above