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

Multiple Choice

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. The ANOVA procedure relies on three important assumptions to be valid:
(1) The data are independent random samples.
(2) The populations are Normally distributed or the sample sizes are large enough.
(3) The populations have the same standard deviation .
$$\sigma$$ In the case of this ANOVA test, which of the following statements about this scenario is correct?

A) Assumption (1) is the only assumption not satisfied.
B) Assumption (2) is the only assumption not satisfied.
C) Assumption (3) is the only assumption not satisfied.
D) All the test assumptions are satisfied.