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Example of Paired T Test for Statistics Students

Suppose a new weight loss program was sponsored by the local health and fitness club in a small town. The program claims to make people lose more than five pounds in a month. Twelve participants were selected and their weights were recorded. After a month of the program their weights were recorded again. It was found that many participants lost some weight. But there was variation. Some lost more and some lost less, and some did not lose any pound at all. The measurements were as follows:

Obs before after
1 217 202.5
2 188 178
3 225 210
4 168 157
5 178 169
6 182 180
7 174.5 163.5
8 161.5 153
9 177.5 178
10 358.5 336
11 181 174
12 210 197.5

Test the claim of the program sponsors at reasonable levels of significance.

We can use calculator to find the paired differences, then find its mean and standard deviation, then standard error of the sample mean difference, and then perform the t-test using t- table. Do this with calculator, formula and t-table.

Solution Preview

For this question you will need to do a paired t test as both data sets come from the same individual, or the "before and after" type of experiment design.

The following formula will be used:

t observed = dbar - md/ sdbar

Where dbar is the average of all difference values between sets, md is equal to 0 (because of paired data), and sdbar is equal to standard deviation/square root n (standard error).

The null hypothesis in this case is that there will not be a difference in mean weight after completion of the weight loss program.

Ho: mean before = mean after.

The alternative hypothesis is that there will be a difference between mean weight before and after the completion of the weight loss program.

Ha: mean before does not equal mean after.

First, find the differences in weight for each individual and then square ...

Solution Summary

A worked through, step-by-step solution for a paired t test design.