In an Experiment on the Effect of Garlic on Blood

Multiple Choice

In an experiment on the effect of garlic on blood lipid concentrations, adult volunteers with slightly elevated cholesterol levels were randomly assigned to one of four treatments taken daily for six months: raw garlic, garlic powder, garlic extract, or a placebo. The participants' LDL levels (low-density lipoprotein, or "bad" cholesterol, in mg/dL) were assessed at the end of the six-month study period. Summary statistics and a partial ANOVA table for this study are shown here.
$$\begin{array}{l}\begin{array} { l c c c } { \text { Treatment } } & \text { Mean } & \text { Standard Deviation } & \text { Sample Size } n \\\text { Raw garlic } & 142 & 22 & 49 \\\text { Garlic powder } & 137 & 25 & 47 \\\text { Garlic extract } & 137 & 22 & 48 \\\text { Placebo } & 133 & 21 & 48\end{array}\\\begin{array} { l c c c c } \text { Source } & \text { df } & \text { Sums of Squares } & \text { Mean Square } & \text { F-Ratio } \\\text { Treatment } &&& 959.46 & \\\text { Error } && 95,457.00 &\end{array}\end{array}$$ The research question is: Do the data provide evidence that the treatments affect the mean LDL level in this population? Based on this ANOVA test, and using a significance level of 0.05, what should you conclude?

A) Reject the null hypothesis and conclude that there is significant evidence that the four treatments do not all lead to the same population mean LDL level after six months.
B) Reject the null hypothesis and conclude that there is significant evidence that raw garlic for six months leads to a higher mean LDL level in this population.
C) Fail to reject the null hypothesis and conclude that there is not enough evidence to say that the treatments influence the population mean LDL level after six months.
D) Do not reach a conclusion because the conditions for ANOVA are not all satisfied in this case.