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

Question 6

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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 BPG0235 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:
 Active  Inactive 1.01.11.00.91.00.51.20.91.21.01.31.01.00.80.71.1\begin{array} { | l | l | } \hline \text { Active } & \text { Inactive } \\\hline 1.0 & 1.1 \\\hline 1.0 & 0.9 \\\hline 1.0 & 0.5 \\\hline 1.2 & 0.9 \\\hline 1.2 & 1.0 \\\hline 1.3 & 1.0 \\\hline 1.0 & 0.8 \\\hline & 0.7 \\\hline & 1.1 \\\hline\end{array} We want to know if there is a significant difference in the relative abundance of the protein BPG0235 between men in the active stage and men in the inactive phase. Therefore, we test the following hypotheses:
?
H0: ?A= ?1 versus Ha: ?A? ?1
Which assumption must be true for the test results to be correct?


A) The population distributions must be roughly Normal.
B) The sample standard deviations must be similar.
C) The population standard deviations must be equal.
D) The same individuals must be measured during an active phase and during an inactive phase.

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