00:01
For this problem, we've had a confidence interval already constructed, where the sample size given for that confidence interval was 40, and this confidence interval was found to be 17 .25 ± 2 .42.
00:21
And this is a confidence interval for population mean, of course, since these numbers are greater than 1, and we want to figure out what our confidence interval would be if our sample size was 160 instead of 40.
00:36
So we want to change this 40 to 160, and get the corresponding confidence interval.
00:44
Okay, so we have this confidence interval here.
00:46
Let's recall something about how a confidence interval is constructed.
00:52
You take your sample mean, whatever it may be, well, that's given to us right here, this is x -bar, and then you add or subtract the margin of error term, which is this term right here, and the margin of error has the following form.
01:10
It is a z -score associated with the level of confidence you want, times sigma, over root n.
01:21
So, if our margin of error is 2 .4, oops, let me use black here, so our margin of error here is then equal to 2 .42, which we know, since this term here is also the margin of error, that is equal to z -score times the population standard deviation over root n.
01:47
And we happen to know what root n is, so n is 40, so we can then get the product of this z -score times sigma...