Researchers Examined a New Treatment for Advanced Ovarian Cancer in a Mouse

Researchers examined a new treatment for advanced ovarian cancer in a mouse model. They created a nanoparticle-based delivery system for a suicide-gene therapy to be delivered directly to the tumor cells. The mice were randomly assigned to have their tumors injected with either the gene -- nanoparticle combination, the gene alone, or some buffer solution (placebo) . The following table shows the tumor fold-increases after two weeks in a total of 29 mice. A fold-increase of 1 represents no change; a fold-increase of 2 represents a doubling in volume of the tumor.
$$\begin{array} { | c | c | c | } \hline \text { Buffer } & \text { Gene } & \text { Gene+Nano } \\\hline 3.3 & 2.7 & 1.1 \\3.8 & 3.0 & 1.1 \\4.1 & 3.3 & 1.2 \\5.4 & 3.4 & 1.4 \\5.4 & 3.9 & 1.8 \\6.8 & 4.3 & 1.8 \\7.0 & 5.3 & 2.1 \\7.8 & 5.6 & 2.1 \\8.1 & 5.6 & 3.5 \\9.1 & & 4.1 \\\hline\end{array}$$ Under the null hypothesis that the three populations have the same continuous distribution, which distribution does the test statistic H have?

A) Approximately a chi-square distribution with 2 degrees of freedom
B) Approximately an F(2, 26) distribution
C) A distribution that cannot be evaluated because the populations may not be Normal
D) Approximately a Normal distribution