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Chapter 8: Problem 65

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. \({ }^{23}\) 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 part (a), do these data give good evidence that on the average nursing mothers lose bone mineral? Explain.

Short Answer

Expert verified
The 99% confidence interval is \([-4.575, -2.599]\), indicating good evidence of average bone mineral loss in nursing mothers.

Step by step solution

01

Identify the Problem

We want to construct a 99% confidence interval for the mean percent change in bone mineral content (BMC) of nursing mothers' spines. We'll use the sample data provided: mean change of \(-3.587\%\) and standard deviation of \(2.506\%\) with a sample size of 47.
02

Find the Critical Value

For a 99% confidence interval, we need to find the critical value \(t^*\) for 46 degrees of freedom (sample size minus 1). Using a t-table or calculator, the critical value \(t^*\approx 2.704\).
03

Calculate Standard Error

Calculate the standard error (SE) of the mean using the formula: \[SE = \frac{s}{\sqrt{n}} = \frac{2.506}{\sqrt{47}} 鈮� 0.3657\].
04

Compute the Confidence Interval

Calculate the margin of error (ME) using the formula: \(ME = t^* \times SE = 2.704 \times 0.3657 鈮� 0.988\). Then, form the confidence interval: \([-3.587 - 0.988, -3.587 + 0.988]\), which gives us \([-4.575, -2.599]\).
05

Interpretation of Confidence Interval

Interpret the interval \([-4.575, -2.599]\). With 99% confidence, we can say that the true mean percent change in BMC for all nursing mothers falls within this interval.
06

Evidence of Bone Mineral Loss

Since the entire confidence interval is below 0, it suggests that, on average, nursing mothers experience a loss in bone mineral content during breastfeeding.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Bone Mineral Content
Bone Mineral Content (BMC) is the measure of the amount of minerals, primarily calcium, found in a certain volume of bone. It reflects bone health and strength. During breastfeeding, some of the calcium required to produce milk may be drawn from a mother's bones, potentially decreasing BMC. Understanding BMC is crucial because it helps researchers assess the impact of breastfeeding on maternal bone health. A decrease in BMC could indicate a temporary or prolonged reduction in bone strength, which is why its measurement is vital in studies involving mothers during their breastfeeding period.
Breastfeeding Research
Breastfeeding research explores the effects of lactation on mothers and infants, with a particular focus on nutrition and health. Researchers often investigate changes in the mother's body during breastfeeding, including alterations in bone mineral content. In studies like the one mentioned, a sample of mothers is analyzed to determine how breastfeeding might affect bone density鈥攁 critical component of maternal health care. Such research is essential in establishing guidelines for maternal nutrition and ensuring the protection of both infant and maternal well-being during the breastfeeding period.
Statistical Inference
Statistical inference is the method used to make predictions or decisions about a population based on sample data. In the exercise, inference is made through a confidence interval, which estimates the range in which the true mean percent change in BMC lies, based on the sample of 47 mothers. The goal of statistical inference is to draw conclusions with a quantifiable level of confidence, in this case, 99%. This makes it a valuable tool in research, providing insights that are scientifically robust and reliable.
Mean and Standard Deviation
The mean and standard deviation are key statistical measures. The mean, or average, provides a central value for the data鈥攊n this case, the average percent change in BMC among breastfeeding mothers was found to be e -3.587%. Standard deviation measures the variability or spread of the data points around the mean. A standard deviation of 2.506% indicates how much the percent change in BMC varies from mother to mother. Both statistics are integral in computing confidence intervals, aiding researchers in drawing meaningful conclusions from their data.

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Most popular questions from this chapter

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