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%.

a. Construct and interpret a 99% confidence interval to estimate the mean percent change in BMC in the population of breast-feeding mothers.

b. Based on your interval from part (a), do these data give convincing evidence that nursing mothers lose bone mineral, on average? Explain your answer.