Question

Asked Jun 26, 2019

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Comparing the bacterial effects of antibacterial and non-antibacterial soap would be (sample n=3)

A)paired t-test

B) indepedent t-test

C) chi square test

why? thank you

Step 1

**Explanation:**

In order to compare the bacterial effects of an antibacterial soap with that of a non-antibacterial soap, the reduction in the percentage of bacteria after using each type of soap can be considered as the parameter of interest. A possible way to carry out the test is as follows:

- Let the study be performed on humans. Let each person in the study start with a particular percentage of bacteria in their hands.
- Assign the subjects randomly to either wash their hands with the antibacterial soap or with the non-antibacterial soap and note the reduction in the percentage of bacteria of each subject.
- Again, ensure the same percentage of bacteria is in their hands, as it was at the very first step.
- Those who previously washed their hands with the antibacterial soap must now wash their hands with the non-antibacterial soap, and vise-versa. Again, note the reduction in the percentage of bacteria of each subject.
- Denote
*x*as the reduction in bacteria percentage after washing with the antibacterial soap and*y*as the reduction in bacteria percentage after washing with the non-antibacterial soap; denote*d*=*x*–*y*. - Use the paired
*t*-test to compare the effects of the two types of soap.

Step 2

**Some constraints:**

The given sample size, *n* = 3 is extremely small. It may not satisfy the assumption of approximate normality, which is required for performing a *t* test of any kind.

However, it is often observed in real life that, if the correlation within the pairs is high, then it is possible to use the paired *t*-test, even if the sample size is very small. Here, the same set of individuals is given both types of treatments- the two kinds of soap, which give two sets of observations. Naturally, the correlation within the pairs can be assumed to be quite high.

Thus, it is recommended to use the **A) paired t-test** for the study, unless any exceptional difficulties arise.

Step 3

**The alternatives:**

Ideally, an independent *t*-test would require two sets of independent individuals, so that one set would receive the antibacterial soap and the other would receive the non-antibacterial soap. However, the study is not likely to be properly representative, if such a small sample size is again divided ...

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