And we want a 95 confidence interval.

So we want to find a 95 confidence interval.

So you look at the two sided, we want a 95 confidence interval, so we're going to look right over here, 95 confidence interval.

When that's the case, the confidence interval itself carries 95 of all possible values for p, so the chances that p lies outside the green confidence interval is 5 , hence, we call it a 95 confidence interval.

What value we will be using for a two sided 95 confidence interval.

Now I want the plus minus term, the two sided confidence interval at a confidence level of 95 .

79.74 is the mean. This is the 95 confidence interval less than a kilogram.

Level of the confidence interval

Now, where does the 1.96 come from? and here's the trick, 1.96 marks the 95 confidence interval.

Given the following set of 10 range measurements, what is the 95 confidence interval for the actual distance?

What's new now is the confidence interval, and the confidence interval is not the same as the variance.

Then factor in the magic number 1.96, which is the two sided 95 confidence interval number for the normal distribution.

And now we get to the confidence interval.

I'm just using that same data to come up with a 95 confidence interval for the actual mean emission for this new engine design.

This is the number we can add or subtract to the mean, so that at 95 confidence the true mean lies within the interval.

My first question for you is, to compute the confidence interval, assuming that we can use a confidence interval to detect outliers in the data.

If you assume a symmetrical confidence interval with five percent confidence, in our magic factor that percentile is 1.96 compute for me in percent the confidence interval for the variable Delta T.

Remember that the width of the confidence interval decreases with the n.

As the sample size approaches infinity, the confidence interval width approaches 0.

As the sample size approaches infinity, what happens to the confidence interval width?

So once again, that gives us a confidence that we got the right interval.

It turns out that the real challenge is not to compute the confidence interval.

Something like this margin of error is the same as the confidence interval width.

We are quite sure we have a confidence interval that's 0.42 wide on both sides.

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Let's now apply what we just learned in the context of computing an actual confidence interval.

In fact, if the standard deviation is σ, then the confidence interval is effectively 1 Nσ.

Let me illustrate this again. For any sample, you know how to compute a confidence interval.

In this margin of error, means what's really been given back is not singular number like 60 , but an interval we call this the confidence interval.

What's the largest number of healthy people out of the 10 where you'd be suspicious and you wouldn't be 95 confident using our 95 5 confidence threshold.

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