Creatinine excretion is a parameter of kidney function. Generally speaking, lower values indicate better health. This depends on body weight. A researcher conducted a study on creatinine excretion in test group and control group to find the efficacy of a new drug. The subjects were randomly divided. He included 100 subjects in each group but for this exercise consider only 10 subjects in each group. The data obtained on creatinine level in these 10 subjects are as follows:

Test group:                                                                                                    16.6   19.8   17.1   17.0   15.6   20.3   24.7   18.5   17.6   22.0

Control group:                                                                                               23.2   22.0   21.9   16.7   14.2  23.2   24.8   25.5   28.1  21.8

Do you think that creatinine excretion was really lower in the test group on average?

To determine whether creatinine excretion was truly lower in the test group on average compared to the control group, we can perform a statistical analysis. We will begin by calculating the mean creatinine excretion for each group and then conduct a hypothesis test.

Let's denote:
- Test group mean: \( \bar{x}_T \)
- Control group mean: \( \bar{x}_C \)

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