00:01
So our question says use the given data to find a minimum sample size required to estimate the population proportion.
00:07
According to the question the margin of error is 0 .044.
00:11
The confidence level is 95 % and of sample proportion p -cap and q -cap are actually unknown.
00:17
So let us write out our parameters.
00:20
We have the margin of error to p .0 .04.
00:24
We have the confidence level beta to be 95%.
00:28
So whenever we find ourselves in a situation where we are trying to get the sample size from a margin of error and we're not given the initial estimate for either p -cap or q -cap, then we can assume a value of p -cap that is equal to 0 .5, which is 50%.
00:47
So this simply implies that if our p -cup is equals to 0 .5, the name is our q -cap is equals to 1 minus 0 .5, which is also gives us 0 .5.
00:57
So by having this, we can be able to substitute the value of p -c -cap and q -cap into our formula.
01:02
So at 95 % confidence in terms, the formula for the margin of error is giving us m -e is equal to 1 .96 times.
01:10
We have the square root of p -cap.
01:13
We have q -cap divided by n.
01:16
So let's substitute our parameters into our formula...