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# Clarification of confidence interval of difference of means

Video transcript

Near 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. I'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. Because 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. It'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. And 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. And 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. Anyway, 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.