Question

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 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.

Short answer

a. Confidence interval is $(-4.569,-2.605)$

b. No, it is due to the fact that interval do not have zero.

Step-by-step solution

Given Information

It is given that $\left(\overline{x}\right)=-3.587$

$\left(s\right)=2.506$

Confidence Level $=99\%$

$n=47$

Calculating Confidence Interval

Confidence mean is calculated as:

$CI=\overline{x}\pm t_{\alpha /2}\times \frac{s}{\sqrt{n}}$

Output of MINTAB is as below:

Hence, there is $99\%$confidence that for breast feeding mothers, mean change in BMC lie between$-4.569\text{and}-2.605.$

Nursing Mothers are losing Bone Mineral or not.

The confidence interval is $(-4.569,-2.605)$. It does not contain $0$.

Hence, it is not concluded that they are losing bone mineral.