00:01
Hey there, welcome to numerade.
00:03
So we are given a random sample of 25 adult americans to see if they support or support or not the proposed changes.
00:14
So let's say the proportion of adults are approximately normal.
00:19
So what would the sample size be? more specifically, how many more adult americans do we need to sample? so with this, what we know here is that it is approximately normal.
00:34
So since it is approximately normal, our sample size times our proportion times 1 minus our proportion must be at least 10.
00:55
So it would have to equal 10 basically.
01:00
N times p times 1 minus p equals 10.
01:06
So this is the equation that we're going to use for parts a and b in order to solve.
01:12
So what we are given here is our sample size of 25, and our proportion is also given to us as 0 .15.
01:33
All right.
01:35
So now using this equation, we're going to solve for n.
01:39
Okay, so let's rearrange this equation here.
01:43
So therefore, we're going to solve for n.
01:48
Equals 10 divided by our proportion times 1 minus our proportion.
02:04
Okay, so we just divide that under 10 over here, proportion times 1 minus proportion.
02:11
So let us plug in our value.
02:17
So n equals.
02:19
So we have the 10 divided by our proportion is 0 .15 times 1 minus 0 .15 is 0 .85.
02:40
So let's see what we get here.
02:45
So we have 10 divided by 0 .15 times .85, which gives us a sample size, rounded up to the nearest integer.
03:01
So we have 78 .43...