00:01
In the first part of the question, the confidence interval given here, so for part a, the confidence interval for the proportion, the lower boundary is 0 .0283 and the upper boundary is 0 .0333 and the confidence level which is given as 90 percent.
00:18
So what we have to find? in order to get the sample size, we're going to use the margin of error formula, so i need the margin of error, and for the confidence interval we know that this is the sample proportion plus the margin of error, or the minus margin of error, so that means the sample proportion plus the margin of error, that gives us the upper boundary, and if i just subtract the margin of error from the sample proportion, i will get the lower boundary, which is this number here.
00:45
Let's add these two simultaneous equations together, and the me values cancel to each other, so we will get the sample proportion, which is the sum of these two numbers, and 0 .0283, and so i'm going to divide this by two to get the p -value here, which is 0 .0308.
01:06
Let's get the margin of error, which is, so i'm going to plug in this value into the one of the equation, let me just use the first equation here, i'm going to plug in this value, and when i subtract from this number, i will get the margin of error, so the margin of error would be 0 .0333 and minus 0 .0308, here we go, this is 0 .0025.
01:32
Let me use the margin of error, so the margin of error, which is equal to sample proportion, okay, and time, sorry, this is the z alpha over 2 times the square root of the sample proportion, 1 minus proportion, and divided by n.
01:47
To leave the n alone here, take the square of the both sides, which is the z alpha over 2 divided by margin of error, and then bracket squared, times p times 1 minus p.
01:57
Let's get the z value, the alpha is 1 minus confidence level, but we need alpha over 2, which means this is 0 .96, divide by 2, which would be 0 .02...