Question

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?
_____________

Answer 1

Answer:

Part A

The probability of the treatment groups mean being greater than the control group mean by 8points or more = (26+8+2)/1000 = 0.036

Part B

Yes, the result is statistically significant because the probability of the difference being 8point or more is less than 5% significant level

Part C

The answers is 0.036 means that there is a very little chance of obtaining difference of 8points or more by random chance. So, if the difference between treatment group mean and control group mean is at least 8 , then the result is significant which means protein shaken is actually helpful in speeding up the weight-10 process