00:01
In this question we have some sample data and i will start by writing out the information given in so n equals as our first one, n is the sample size so that's 42, is it greater than 30? yes.
00:19
X bar is the sample mean so that would be 13 .5, s is the sample standard deviation so that's 4 .8.
00:30
We also want our degrees of freedom df which is n minus 1 so that's 41.
00:38
From this we want t, the critical value.
00:42
Okay so i'm going to pause that and write out the formula for a confidence interval for a population mean.
00:50
It's x bar, the point estimate, our best guess, plus and minus a margin of error.
00:57
We're going to be using ts over root n so s over root n or sigma over root n always makes an appearance, that's the standard error.
01:06
T is our critical value.
01:08
It doesn't have to be t though, it could alternatively be z.
01:12
Z is preferable but you tend to use t if population standard deviation, sigma, is unknown and you have a small sample.
01:26
Now really this sample is large enough that you could use z and get a pretty decent answer.
01:31
As the sample size increases, s becomes a better estimate for the population standard deviation.
01:38
The cutoff point for when you just use z anyway varies depending on your teacher or the textbook but they want t here so we will use t...