Percentages of ideal body weight were determined for 18 randomly selected insulin-dependent diabetics and are shown below. A percentage of 120 means that an individual weighs 20% more than his or her ideal body weight; a percentage of 95 means that the individual weighs 5% less than the ideal.
107 119 99 114 120 104 88 114 124
116 101 121 152 100 125 114 95 117 (%)
a) Find a 99.8% confidence interval for the true mean percentage of ideal body weight for the population of insulin-dependent diabetics. Does this confidence interval contain the value of 100%? What does the answer to this question tell you?
b) Construct an upper 99.5% bound for the mean percentage of ideal body weight for the population of insulin-dependent diabetics. Explain what the bound means.