00:01
All right, in your question, it says you measure 42 textbooks and find they have a mean weight of 51 ounces.
00:06
So i listed n equals 42 for my sample size.
00:10
The mean of our sample, which we call x bar, is 51 ounces.
00:14
And the standard deviation of the population is 3 .3.
00:18
You're to construct a 99 % confidence interval.
00:21
And i've listed here how you create a 99 % confidence interval for a sampling distribution of a sample mean.
00:30
You take your sample mean, add or subtract a critical value times, sometimes this is our, well, it is your standard error, but we're going to have to find it from the population standard deviation.
00:43
And the formula for that would be this standard deviation divided by square root of sample size.
00:49
So the only thing i don't think i've explained is how you find this critical value, z star.
00:55
What you're doing is trying to, when you create a 99 % confidence interval, you're trying to, block off the middle 99 % of a normal distribution.
01:06
And the z star value is the z score for the upper cutoff.
01:11
Now i have found that with technology.
01:14
I used a ti 84 and i used a program called inverse normal.
01:20
And when you do this, you have to include this little tail down here, which would be half a percent or 0 .005.
01:31
In decimal, combine it with your 99%, for you're actually looking, or using the calculator to figure out the area of 0 .995%, because it always goes from the bottom up.
01:45
Now i'm going to show you how you could do that on a z table as well.
01:50
A z table, you can see i've highlighted the two closest values to 0 .995...