Fitness experts advise people who want to lose weight to drink protein shakes after workout sessions, because it helps build muscle mass and speeds up the weight-loss process. To test the effectiveness of protein shakes in losing weight, 200 adults between the ages of 25 and 40 years were divided equally into two groups: a treatment group and a control group. The treatment group was asked to drink a protein shake after every workout session for a period of 6 months. The subjects’ weights were noted before and after the treatment. The results showed that the mean change in the amount of weight lost by the treatment group is 8 points more than that of the control group. To test whether the results could be explained by random chance, researchers created a table that summarizes the results of 1,000 re-randomizations of the data with differences of means rounded to the nearest 2 points.

Consider the significance level to be set at 5%, so results less than 5% can be considered statistically significant.

Treatment Group Mean − Control Group Mean Frequency
-12 1
-10 10
-8 28
-6 58
-4 125
-2 184
0 201
2 186
4 114
6 57
8 26
10 8
12 2

Part A
Determine the probability of the treatment group’s mean being greater than the control group’s mean by 8 points or more.

Part B
Is the result statistically significant? Explain your answer.

Part C
What does your answer mean in the context of drinking protein shakes while on a weight-loss program?