Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers measured the percent change in bone mineral content (BMC) of the spines of 47 randomly selected mothers during three-months of breast feeding. The mean change in BMC was -3.587% and the standard deviation was 2.506%. Please show all of your work.
(a) Construct and interpret a 99% confidence interval to estimate the mean percent change in BMC in the population. (use the 4-step process: State. Plan. Do. Conclude)
(b) Based on your interval from (a), do these data give good evidence that on the average nursing mothers lose bone mineral? Explain.