Samplin Distribution of the Mean Difference Conceptual Overview: Explore the sampling distribution of the difference between two means. The mean of a random variable has a sampling distribution. 80 does the difference between two means. The top figure below shows the distribution of observations for two different groups. The figure in the middle shows the sampling distribution of their respective means. The bottom graph shows the resulting sampling distribution of the difference between the two means. If 0 is in either of the far tails in the bottom distribution, then there likely is a significant difference between the two means. The tail including 0 is marked in darker green. Drag the red distribution in the top graph to change the difference between the two groups. Observe how the distance between the two sampling distributions of the means (middle graph) changes. Observe how the sampling distribution of the mean difference (bottom graph) moves correspondingly. Pay special attention to the location of 0 which indicates no difference in the means of the two groups. DISTRIBUTION OF OBSERVATIONS FOR TWO GROUPS SAMPLING DISTRIBUTION FOR THE MEAN OF EACH GROUP 1 50 200 250 300 350 400 450 SAMPLING DISTRIBUTION OF THE DIFFERENCE BETWEEN BOTH MEANS -1 50 -100 -50 0 50 100 150 1. Move the red distribution at the top so that it aligns with the blue distribution. Now look at the green distribution at the bottom. How would you best interpret the green (bottom) distribution? a. The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are not statistically different. b. The distribution of differences between the sample means of each group has a mean at or near 325 making it likely the two groups are not statistically different. c. The distribution of differences between the sample means of each group has a mean at or near zero making it likely the two groups are statistically different. d. The distribution of differences between the sample means of each group has a mean at or near 325 making it likely the two groups are statistically different. V l 2. Now move the red distribution at the top to the right so that its mean is approximately 375 and then look at the middle and bottom distributions. Based on the location of 0 in the bottom distribution (meaning no difference in the means) what is the best conclusion? a. A mean difference of 0 is very likely and therefore the idea that the two groups are the same should be rejected. b. A mean difference of 0 is very unlikely and therefore the idea that the two groups are the same should not be rejected. c. A mean difference of 0 is very unlikely and therefore the idea that the two groups are the same should be rejected. d. A mean difference of 0 is very likely and therefore the idea that the two groups are the same should not be rejected. Vl