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Chapter 8: Q. 67 (page 519)

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 47randomly selected mothers during three months of breastfeeding. 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.

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

Short Answer

Expert verified

(a) We are 99%confident that the true population mean is between -4.5754%and -2.5986%.

(b) Yes, the data give good evidence that on average nursing mothers lose bone mineral.

Step by step solution

01

Part (a) Step 1: Given Information 

Given

x炉=-3.587

s=2.506

02

Part (a) Step 2: Explanation

Determine the t-value by looking in the row starting with degrees of freedom df=n-1=47-1=46>40and in the row with c=99%in table B:

t*=2.704

The margin of error is then:

localid="1650086388315" E=t*路sn=2.704脳2.50647鈮�0.9884

Then the confidence interval becomes:

localid="1650086498431" -4.5754=-3.587-0.9884=x炉-E<渭<x炉+E=-3.587+0.9884=-2.5986

We are 99%confident that the true population mean is between -4.5754%and -2.5986%.

03

Part (b) Step 1: Given Information 

Given

x炉=-3.587

s=2.506

04

Part (b) Step 2: Explanation 

Confidence interval found in part (a):

-4.5754<渭<-2.5986

Since the confidence interval does not contain 0and lies completely below 0, the data gives good evidence that on average nursing mothers lose bone mineral.

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