A study examined survival of gastrointestinal pathogens (such as salmonella and E. coli) in seven different beverages. The beverages tested were cola, lemonlime mixer, diet cola, beer, wine, milk, and water. Bacteria were placed in the different beverages, over multiple trials, and the change in the number of bacteria was recorded after four hours. The mean number of bacteria had increased slightly in milk and water (not good for stomach health!) and had decreased slightly in all three soft drinks and beer, but none of these changes were significantly different from the others. The only significant difference was a dramatic decrease in bacteria in the wine, with a mean change significantly different (and better) than all the others. The researchers were testing, at a 5% significance level, to see if there was a difference in mean change between the seven beverages.

(a) What are the two main variables in this study? Identify each as categorical or quantitative. 

(b) What are the degrees of freedom for groups in the analysis of variance test? 

(c) In the ANOVA test, is the p-value above 0.05, below 0.05, or is it impossible to tell from the information given? 

(d) State the generic conclusion and the conclusion in context, or state that it is impossible to tell.