1. Lactation promotes a temporary loss of bone mass to provide adequate amounts of calcium for milk reproduction. The paper ["Bone Mass is Recovered from Lactation to Postweaning in Adolescent in Adolescent Mothers with Low Calcium Intakes"](https://www.ncbi.nlm.nih.gov/pubmed/15531682) gave the following data on total body bone mineral content (TBBMC) (g) for a sample both during lactation (L) and in the postweaning period (P). ```{r} TBBMC <- read.table(header = T, text=" Subject Lactation Postweaning 1 1928 2126 2 2549 2885 3 2825 2895 4 1924 1942 5 1628 1750 6 2175 2184 7 2114 2164 8 2621 2626 9 1843 2006 10 2541 2627 ") TBBMC ``` i) Compute the differences in the TBBMC between "during lactation" and "postweaning period". Assign this new column into the same data set. ii) Compute summary statistics (mean and standard deviation) on this new column of differences. iii) Compute a 95\% confidence interval for the mean difference in TBBMC between "during lactation" and "postweaning period". iv) Based on the computed confidence interval, does the data suggest mean TBBMC is different between "during lactation" and "postweaning period". v) Compute the (incorrect) two-sample t-interval on the data. See Week 10 lesson on how to do this. Does the (incorrect) two-sample t-interval lead to the same conclusion that you obtained in part (iv)? Explain.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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1. Lactation promotes a temporary loss of bone mass to provide adequate amounts of calcium for milk reproduction. The paper ["Bone Mass is Recovered from Lactation to Postweaning in Adolescent in Adolescent Mothers with Low Calcium Intakes"](https://www.ncbi.nlm.nih.gov/pubmed/15531682) gave the following data on total body bone mineral content (TBBMC) (g) for a sample both during lactation (L) and in the postweaning period (P).

```{r}
TBBMC <- read.table(header = T, text="
Subject Lactation Postweaning
1 1928 2126
2 2549 2885
3 2825 2895
4 1924 1942
5 1628 1750
6 2175 2184
7 2114 2164
8 2621 2626
9 1843 2006
10 2541 2627
")
TBBMC
```

i) Compute the differences in the TBBMC between "during lactation" and "postweaning period". Assign this new column into the same data set.
ii) Compute summary statistics (mean and standard deviation) on this new column of differences.
iii) Compute a 95\% confidence interval for the mean difference in TBBMC between "during lactation" and "postweaning period".
iv) Based on the computed confidence interval, does the data suggest mean TBBMC is different between "during lactation" and "postweaning period".
v) Compute the (incorrect) two-sample t-interval on the data. See Week 10 lesson on how to do this. Does the (incorrect) two-sample t-interval lead to the same conclusion that you obtained in part (iv)? Explain.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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