Applying a Level of Significance In this activity, you’ll study the data from two experiments. For each data set, you will determine whether the difference of means between the treatment group and the control group is statistically significant and interpret the result in the context of the situation. 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 (-12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12)

Frequency ( 1, 10, 28, 58, 125, 184, 201, 186, 114, 57, 26, 8, 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?