00:01
Okay, so we're looking at a question about confidence intervals.
00:03
Our sample size is 42.
00:06
Our sample mean is 77 .4.
00:11
Secretly, we know that the population mean is 75.
00:15
We also know the population standard deviation is 10.
00:18
The first thing we need to do here is make some confidence intervals.
00:22
So the formula for a confidence interval for a population mean mean is x bar, point estimate, plus and minus the margin of error, z sigma over root n.
00:33
We've been given z here for the different levels of confidence, so all we have to do is put these values in.
00:40
So for the 75 % confidence interval, it is 77 .4, plus and minus, so we're using 1 .15 multiplied by 10 over root 42.
00:52
So if i just do that, if i take that away away from the point estimate, i get the lower bound of 75 .63.
01:07
If i add it on, i get the upper bound, 79 .17.
01:15
Okay.
01:16
And for the 95 % confidence interval, same x bar, different confidence, different critical value, 1 .96, same standard deviation, same sample size.
01:29
So, just repeating my calculation with these new values.
01:38
Now my lower bound, make some space, is 74 .38.
01:47
My upper bound is 80 .42.
01:54
So you can see an increase in the confidence increases the width of the interval.
01:58
And you just need to drag your upper and lower bounds on those little diagrams they've given you to get those...