00:01
In this situation, they tell us that a poll reported 36 % approval rating for a politician with a margin of error of one percentage point.
00:09
So they want to know how many voters should be sampled for a 90 % confidence interval.
00:18
So the way to calculate this is use the equation that the sample size that we need.
00:25
Let me do that in yellow.
00:26
The sample size that we need is equal to the z value corresponding to the i'm going to write it the traditional way, alpha halves, and divided by the margin of error that we want squared times the proportion that we have of the population times one minus the proportion.
00:50
That's the way we calculate the sample size.
00:53
So all we need to do is find the different values of z corresponding to these zs come from the confidence interval.
01:02
So for 90%, the alpha, alpha is 1 minus 0 .90 which is 0 .10.
01:12
So we want the c value of half of that, 0 .05.
01:20
And that's what we're going to do.
01:23
So divided by the margin of error.
01:25
Here the margin of error is 1 percentage point.
01:29
The p is 0 .36 and this is 1 minus 0 .36.
01:36
To find that z value we use a c table or you can use a calculator.
01:40
In this case i'm going to use a calculator and i'm going to use the ti 84 which is a very popular high school calculator let's clear this up so you go to distributions here the normal distribution and we want to find that because 0 .05 is the area we're going to use the inverse normal to find z values so we're going to use the inverse normal to find z values the area is 0 .05 the mean in this case we're going to use the standardized version and which is a mean of zero and a standard deviation of one and we want this on the right side and there we go and this gives us the c value of 1 .64 48 49 so the sample size is 1 .645 which is the traditional way you use it let's make sure that is 645 yes divided by 0 .01 squared times point 36 times 1 minus 0 .36 and that is a sample size of 6 ,235.
03:09
You always want to round these up not just rounded you want to round them up.
03:15
So what that will be the sample for the first case for one for two and for three you're going to do the same thing so i'm just going to copy it so let's just copy this but the z value changes the z value changes.
03:33
So in the case of a 95 % confidence interval, these are very popular and usually most students i recommend that you know them by rot...