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.6 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 all nursing mothers. Suppose that the percent change in this population has standard deviation 2.5%. Make a stemplot of the data to verify that the data 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
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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.6 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 all nursing
mothers. Suppose that the percent change in this population has standard deviation 2.5%. Make a stemplot
of the data to verify that the data follow a
a 0 and a 0 stem because there are both positive and
negative values.)
(b) Use a 99% confidence
percent change in the population
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