Breastmilk and Antioxidants.There is convincing evidence that breastmilk containing antioxidants is important in the prevention of diseases in infants. Researchers A. Xavier et al. studied the effects of storing breastmilk on antioxidant levels in the article "Total Antioxidant Concentrations of Breastmilk-An Eye-Opener to the Negligent" (Journal of Health, Population and Nutrition, Vol. 29, No. 6, pp. 605-611). Samples of breastmilk were taken from women and divided into fresh samples that were immediately tested and the remaining samples that were stored in the refrigerator and tested after 48 hours. A hypothesis test is to be performed to decide whether, on verage, stored breastmilk has a lower total antioxidant capacity.

a. identify the variable.

b. identify the two populations:

c. identify the pairs

d. identify the paired-diffenence variable.

e. determine the null and allernative hypotheses.

f. classify the hypothesis test as nwo tailed, left tailed, or right tailed.

Breastmilk and Antioxidants.There is convincing evidence that breastmilk containing antioxidants is important in the prevention of diseases in infants. Researchers A. Xavier et al. studied the effects of storing breastmilk on antioxidant levels in the article "Total Antioxidant Concentrations of Breastmilk-An Eye-Opener to the Negligent" (Journal of Health, Population and Nutrition, Vol. 29, No. 6, pp. 605-611). Samples of breastmilk were taken from women and divided into fresh samples that were immediately tested and the remaining samples that were stored in the refrigerator and tested after 48 hours. A hypothesis test is to be performed to decide whether, on verage, stored breastmilk has a lower total antioxidant capacity.

Identify the variable in the study.

A variable is an attribute or the characteristic that can be measured. The value of the variable may differ for each and every unit. That is, a variable is defined as the characteristic which is recorded for each case.

From the given description, the variable is "total antioxidant capacity" because the outcome for each attempt can be measured and this value may vary for each and every attempt.

Identify the two populations:

Population:

The population is the complete set of people who are considered for the study.

Therefore, the two populations in the study are "fresh breastmilk" and "stored breastmilk".

Identify the pairs.

Here, the pair is a "women stored breastmilk and fresh breastmilk" because the samples of breastmilk taken from women and divided into fresh breastmilk and stored breastmilk.

Identify the paired difference variable.

The paired difference variable is "the difference between the antioxidant capacity of stored breastmilk and the antioxidant capacity of fresh breastmilk". That is,

$\text{Paired difference variable}=\left(\begin{array}{l}\text{Antioxidant capacity of stored breastmilk -}\\ \text{Antioxidant capacity of stored breastmilk}\end{array}\right)$

State the null and alternative hypotheses.

Null hypothesis:

$H_0:{\mu }_S={\mu }_F$

That is, there is no between the antioxidant capacity of stored breastmilk and the antioxidant capacity of fresh breastmilk.

Alternative hypothesis:

$H_a:{\mu }_s<{\mu }_F$

That is, the antioxidant capacity of stored breastmilk is less than the antioxidant capacity of fresh breastmilk.

Classify the hypotheses test as two tailed, left tailed, or right tailed.

From part (e), it is clear that the hypotheses test as left tailed test because the antioxidant capacity of stored breastmilk is less than the antioxidant capacity of fresh breastmilk.