Two diets are compared for the treatment of diarrhea in children in a developing country.

One diet is the "Western standard of care," which is based on a soy formula and is known to be effective. The other is local diet, which is much less expensive and easier to administer. This local diet consists primarily of kitchri and yogurt. Children with severe, persistent diarrhea were recruited to the study and then randomized to either the Western or local diet.

One outcome measure that investigators are interested in is "Stool frequency (#/day) at Day 5." (For simplicity, we will just call this stool frequency.) For children with diarrhea, a lower stool frequency is desirable.

Investigators are interested in whether the average stool frequency is the same in the two diet groups or if there is evidence that the average stool frequency is different. The following are the hypotheses:

H0:west=local

Ha:westlocal

The average stool frequency in the Western diet group was 3.7 stools/day, and the average stool frequency for the local diet group was 4.3 stools/day. The p value was p=0.35 for testing the average stool frequency for the two groups equal.

A colleague makes this statement after reviewing the results: "I see the p value for this study is greater than 0.05 and not significant (at the alpha=0.05 level). That means that we have evidence that the two average stool frequencies are the same in the two diet groups. We've shown there is no difference between the Western diet and the local diet for the treatment of diarrhea in children."

which is the best response

1. The colleague was not correct. When a p value is greater than 0.05 (and not significant), we can conclude only that the two diets COULD be the same with respect to stool frequencyin this example, we should not conclude that the true mean stool frequency in the two diet populations is the same.

2. The colleague was correct. When a p value is greater than 0.05 (and not significant), we can conclude the study has shown the two treatments (diets) are the same (i.e., the two mean stool frequencies are the same).

3. The colleague was not correct. When a p value is greater than 0.05 (and not significant), we can conclude the stool frequencies are the same in the two groups but can't conclude that it was due to the diets