16.5 It is claimed that a new diet will reduce a person’s weight by 4.5 kilograms, on average, in a period of 2 weeks. The weights of 10 women were recorded before and after a 2-week period during which they followed this diet, yielding the following data:

Woman Weight Before Weight After 123456789 10 58.5 60.3 61.7 69.0 64.0 62.6 56.7 63.6 68.2 59.4 60.0 54.9 58.1 62.1 58.5 59.9 54.4 60.2 62.3 58.7 Use the sign test at the 0.05 level of significance to test the hypothesis that the diet reduces the median weight by 4.5 kilograms against the alternative hypothesis that the median weight loss is less than 4.5 kilograms.