00:01
So we want to find the sample size for three different problems.
00:02
And our first one, we want the margin of air to be no more than 4%.
00:07
And we want to have 90 % confidence.
00:11
And so we know the margin of air comes from that z value, and that z value is 1 .645 times, and we're going to take the square root of, and our estimate will be 0 .5, since we don't have any other guess, and our n, and we want that to basically equal 0 .04.
00:28
And in doing our algebra, we'll find that the square root of n is equal to 1 .645 times in the square root of 0 .5 times 0 .5 is 0 .5.
00:40
And then we would divide those sides by 0 .04.
00:43
And finally, we would square both sides.
00:46
So then we can use that generalization.
00:48
So that's what i will use for my other problems as well.
00:52
And i can just do some substitution.
00:53
But i don't like to memorize formulas.
00:55
So 1 .645 times that 0 .5 divided by the 0 .04, and then we'll square that quantity.
01:05
And that gives me n being, and it comes out to be 422 .8, and we will round that up to 423.
01:15
That sample size will guarantee us that we'll have no more than a margin of error 4%.
01:21
Then on part b, we just want to change that to be a 993...