Clarification of confidence interval of difference of means

0:00Near the end of the last video, I wasn't as articulate as I would like to be. Mainly because I think 15 minutes into a video my brain starts to really warm up too much. But what I want to do is restate what I was trying to say. We got this confidence interval.

0:16I'll rewrite it here. I'll just restate the confidence interval. So there's the 95% confidence interval for the mean of this distribution. So, the mean of that distribution, we got as being 1.91 plus or minus 1.21. And near the end of the video I tried to explain why that is neat.

0:54Because here we have this confidence interval for this weird mean of the difference between the sampling means. So it seems kind of confusing. But I just want to restate what we saw in previous videos. This thing right over here, the mean of the difference of the sampling means, we saw two or three videos ago.

1:17It's the same thing as the mean of the difference of the means of the sampling distributions. And we know that the mean of each of the sampling distributions is actually the same as the mean of the population distributions. So this is the same thing as the mean of Population One minus the mean of Population Two.

1:43And this was the neat result about the last video. This isn't just a 95% confidence interval for this parameter right here. It's actually a 95% confidence interval for this parameter right here. And this is the parameter that we really care about. The true difference in weight loss between going on the low-fat diet and not going on the low-fat diet.

2:10And we have a 95% confidence interval that that difference is between 0.7 and 3.12 pounds. Which tells us that we have a 95% confidence interval that you're definitely going to lose some weight. We're not 100% sure. We're confident that there's a 95% probability of that.

2:30Anyway, hopefully that clarifies it a little bit. I didn't want to confuse you too much with that bungled language that I had at the end of the last video.