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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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Most popular questions from this chapter

Exercises 53 and 54 refer to the following setting. The table below displays the number of accidents at a factory during each hour of a 24-hour shift (1  1 a.m).

53. Accidents happen (1.2, 3.1)
(a) Construct a plot that displays the distribution of the number of accidents effectively.
(b) Construct a plot that shows the relationship between the number of accidents and the time when they occurred.
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(d) Describe something that the plot in part (b) tells you about the data that the plot in part (a) does not.

I collect an SRS of size n from a population and compute a 95%confidence interval for the population proportion. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data?

(a) Use a larger confidence level.

(b) Use a smaller confidence level.

(c) Increase the sample size.

(d) Use the same confidence level, but compute the interval n times. Approximately5% of these intervals will be larger.

(e) Nothing can guarantee absolutely that you will get a larger interval. One can only say that the chance of obtaining a larger interval is 0.05.

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