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 tumor 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. For reference, a fold-increase of 1 represents no change; a 2 represents a doubling in volume of the tumor.
- $$\begin{array} { | r | r | r | } \hline \text { Buffer } &\text { Gene } & \text { Gene+Nano } \\\hline 9.1 & 5.6 & 4.1 \\8.1 & 5.3 & 3.5 \\7.8 & 5.6 & 2.1 \\7.0 & 4.3 & 2.1 \\6.8 & 3.9 & 1.8 \\5.4 & 3.4 & 1.8 \\5.4 & 2.7 & 1.2 \\4.1 & 3.0 & 1.1 \\3.8 & 3.3 & 1.1 \\3.3 & & 1.4 \\\hline\end{array}$$ We want to test the null hypothesis that there is no difference in population mean tumor fold-increase for the three treatments. Based on this ANOVA test, and using a significance level of 0.05, what should you conclude?

A) The population mean fold-increases for gene therapy, combination therapy, and placebo are significantly different from one another.
B) The population mean fold-increases for gene therapy, combination therapy, and placebo are not significantly different.
C) The population mean fold-increase for the combination (gene + nano) therapy is significantly less than the population mean fold-increase with the placebo (buffer) .
D) There is significant evidence that the population mean fold-increases with the gene therapy, combination therapy, and placebo are not all the same.