00:01
All right, and your question, you're told that the mean birth weight is 3 ,103 grams.
00:06
We have a standard deviation of 673 grams, a sample size of 200, and we're supposed to construct a 98 % confidence interval.
00:16
A confidence interval is found by taking the statistic.
00:21
I'm going to put an arrow on that.
00:24
We take our statistic, which is our mean, 3 ,000, well, i'll just put the symbol there for now.
00:30
We take our mean plus or minus a critical value which is given the symbol z star times the standard error and the standard error for distribution of means is to take the standard deviation divided by the square root of our sample size okay so the mean we know is 3 ,103 this critical value z star it's actually a z score that blocks off the middle 98%, the upper z score.
01:07
So we can find that in two different ways, technology or a table, but either way we look at or we include this tail, which would be 1%, or 0 .01.
01:21
Combine those two, that makes 99%.
01:23
I'm going to be looking for 0 .99 on a z table.
01:28
So 0 .99 is found in the middle here between these two values.
01:33
It's a little bit past the middle as you can see and that would be 2 .3 2 and since it's a little bit past the middle it would have to be i'm going to estimate it to 2 .326 so that's our critical value you could also use a technology program called inverse norm where you just type in your area 0 .9991 for the normal model and you would get approximately 2 .326 as well.
02:08
Okay, now we know our critical value, 2 .36.
02:13
Let's type in our, we're going to have our standard deviation of 673 divided by the square root of 200 for our standard error.
02:24
Okay, so to finish our confidence interval, all i need to do is take this 3 ,103 minus this multiplication, and i'll get my lower boundary...