00:01
So our question says you want to obtain a sample to estimate a population proportion.
00:04
At this point in time, you have no reasonable preliminary estimation for the population proportion.
00:08
You would like to be 95 % confident that you estimate is redeem 0 .05, which is 5 % of the true population proportion.
00:15
How large of a sample is required? so our margin of error, which is m .e, is equals to 5%, which is 0 .05.
00:26
And according to our question, we don't have an initial estimation for the population proportion.
00:29
Now, whenever we want to get the margin, we want to work on the margin of error related to sample size.
00:35
And we don't have an initial value for population proportion or we want to construct a confidence in terms of a population proportion.
00:42
Now, we do have an initial estimation for our sample proportion.
00:45
We can assume a proportion of 50%, which is 0 .5, for either the sample proportion or the population proportion, it works perfectly fine.
00:53
So in this case of us, our population proportion, the estimation, the estimated value for the population proportion, and as p is going to be 0 .5 which is 50 % here so the formula for the margin of error at 95 % confidence interval is given us n e is equal to 1 .96 times we have the square root of p times q divided by n so our q in this case is going to be 1 minus p and that's going to be 1 minus 0 .5 which gives us 0 .5 so let so let let us substitute all of our parameters into the formula we have the that the margin of error is 0 .05 is equal to 1 .96 times we have the square root of 0 .5 times 0 .5 divided by n so we have 0 .05 is equal to 1 .96 times so we have the square roots of 0 .5 times 0 .5 divided by the square root of n so we have 0 .05 is equal to so 1 .96 times 0 .05 times 0 .05 in a square root we have that to give us 0 .98 divided by square root of n.
02:08
So the next step is for us to cross multiply...