00:01
So in this question, we are being asked about making confidence intervals for the population mean.
00:11
And so we're only being asked here about part d.
00:15
And part d is saying, you know, suppose we, here sigma is the population standard deviation.
00:25
But suppose we don't know that, we have instead, we have a sample standard deviation.
00:31
And suppose it's 16.
00:33
And it asks us to reconstruct some confidence intervals.
00:35
So remember that normally, in your confidence interval, we take our sample mean and your confidence interval is x plus or minus some z value times sigma over root n.
00:47
But sometimes you don't have sigma, like in this case.
00:49
So then we just do the next best thing.
00:51
We just replace it with the sample standard deviation, s, s over root n.
01:01
So what's the difference here? the big difference is that this normally, when you draw it and you use sigma, everything's kind of normally distributed.
01:12
Your z here can be kind of the appropriate normal distribution percentile corresponding to the right size of a confidence interval.
01:22
But here, this thing is going to be using a t distribution.
01:26
So here we want to go and go grab student t distribution.
01:33
I'm going to use a calculator for this.
01:34
Go and plug in the number of, so we'll do these, i guess, we'll do the kind of pieces differently.
01:39
First one is n equals 75.
01:42
So we care about using a student t distribution with 24 degrees of freedom.
01:47
And we want to go, and i'm going to go compute a quantile.
01:52
We want the 90th percentile confidence interval.
01:55
So we want a 95th percentile, we want a 95th percentile quantile, right? that'll give us a 90th percentile confidence interval or a 90 % confidence interval...