Discussion:
Q. Bone loss by nursing mothers. 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 mineral content of the spines of 47 mothers during three months of breast-feeding. Here are the data:
-4.7 -2.5 -4.9 -2.7 -0.8 -5.3 -8.3 -2.1 -6.8 -4.3
2.2 -7.8 -3.1 -1.0 -6.5 -1.8 -5.2 -5.7 -7.0 -2.2
-6.5 -1.0 -3.0 -3.6 -5.2 -2.0 -2.1 -5.6 -4.4 -3.3
-4.0 -4.9 -4.7 -3.8 -5.9 -2.5 -0.3 -6.2 -6.8 1.7
0.3 -2.3 0.4 -5.3 0.2 -2.2 -5.1
(a) The researchers are willing to consider these 47 women as an SRS from the population of al nursing mothers. Suppose that the percent change in this population has standard deviation SD = 2.5 %. Make a stem-plot of the data to see that they appear to follow a Normal distribution quite closely. (Don't forget that you need both a 0 and a -0 stem because there are both positive and negative values.)
(b) Use a 99% confidence interval to estimate the mean percent change in the population.