Some chronic conditions produce episodes of severe flare-ups ("active" stage) between healthy periods ("inactive" stage) . The active stage often necessitates immediate medical treatment. Researchers looked for biomarkers that might help identify these active stages. Here are data on the relative abundance of the protein BPG0199 in two independent random samples of men with the same chronic condition, 7 men in the active phase and 9 men in the inactive phase:
$\begin{array} { | l | l | } \hline \text { Active } & \text { Inactive } \\\hline 2.6 & 1.2 \\\hline 2.7 & 2.1 \\\hline 2.0 & 1.8 \\\hline 2.4 & 1.5 \\\hline 1.9 & 1.9 \\\hline 1.4 & 3.2 \\\hline 1.8 & 1.3 \\\hline & 1.9 \\\hline & 1.6 \\\hline\end{array}$ We want to know if there is a significant difference in the relative abundance of the protein BPG0199 between men in the active stage and men in the inactive phase. Therefore, we test the following hypotheses:
?
H₀: ?_A= ?₁ versus H_a: ?_A? ?₁
Which assumption must be TRUE for this test result to be correct?

Question

Some chronic conditions produce episodes of severe flare-ups ("active" stage) between healthy periods ("inactive" stage) . The active stage often necessitates immediate medical treatment. Researchers looked for biomarkers that might help identify these active stages. Here are data on the relative abundance of the protein BPG0199 in two independent random samples of men with the same chronic condition, 7 men in the active phase and 9 men in the inactive phase:

\begin{array} { | l | l | } \hline \text { Active } & \text { Inactive } \\\hline 2.6 & 1.2 \\\hline 2.7 & 2.1 \\\hline 2.0 & 1.8 \\\hline 2.4 & 1.5 \\\hline 1.9 & 1.9 \\\hline 1.4 & 3.2 \\\hline 1.8 & 1.3 \\\hline & 1.9 \\\hline & 1.6 \\\hline\end{array}

We want to know if there is a significant difference in the relative abundance of the protein BPG0199 between men in the active stage and men in the inactive phase. Therefore, we test the following hypotheses:
?
H₀: ?_A= ?₁ versus H_a: ?_A? ?₁
Which assumption must be TRUE for this test result to be correct?

Quizplus · Accepted Answer

For comparing means between two independent samples, as is the case here, it's crucial that the population distributions from which these samples are drawn are roughly Normal. This assumption ensures the validity of the test results, especially when using parametric tests like the t-test. Assumptions about the individuals being the same in both groups (A) or about the equality of population standard deviations (B) are not necessary for independent samples tests. While similarity in sample standard deviations (C) can be beneficial, it's the underlying population distributions' normality (D) that's a key assumption for the validity of many statistical tests comparing means.

Some Chronic Conditions Produce Episodes of Severe Flare-Ups ("Active" Stage)