00:01
So the admissions director wants to estimate the mean age of students enrolled in college.
00:07
So i'm going to draw an image.
00:10
We're trying to figure out the mean age of students enrolled in college.
00:15
And we want to be within 0 .75 of a year of the population means.
00:22
So we are allowed to go 0 .75 below or 0 .75 above when we estimate.
00:32
So that .75 is representing our margin of error.
00:40
We are going to assume the population of ages is normally distributed, so therefore we can draw a bell -shaped or normal curve.
00:53
And we want to determine the minimum sample size, so we are trying to calculate n.
01:02
Required so that we can construct a 95 % confidence interval.
01:07
So our confidence interval is 0 .95.
01:13
And we are going to assume that the population standard deviation, which would be represented by sigma, is 1 .5.
01:25
So in order to do this, we are going to need to apply a formula.
01:29
And the formula will be that the minimum sample size is equal to the quantity of the critical z score multiplied by that population standard deviation divided by the margin of error quantity squared.
01:51
So we now know the e value and the sigma value.
01:56
So we can fill in 0 .75 for e.
02:03
And we could fill in 1 .5 for sigma, but yet we still need that critical z value associated with this 95 % confidence interval.
02:17
So what we're going to do is we're going to go back to our bell -shaped curve, and since we are talking about a 95 % confidence interval, we are talking about 0 .95 as the area of the center of that curve.
02:31
Now, since the normal curve has to total up to one, this tail on the left would represent 0 .025, and the tail on the right would represent 0 .025.
02:44
And that critical z represents the lower boundary and the upper boundary of that confidence interval.
02:54
So in order to find that critical z, we are going to use our inverse norm feature.
03:03
On our graph and calculator...