00:01
In this question we've got two hypotheses, p is 0 .20 versus p is not 0 .20, so it's a two -tailed test.
00:14
So we sample size 350 for a sample proportion of 0 .28.
00:22
So first of all let's construct a 99 % confidence interval.
00:26
So for a confidence level of 0 .99 that's going to give us the probability that z is greater than the z multiplier is 1 minus 0 .99 over 2 or 0 .005.
00:40
This gives us a z multiplier of 2 .5758.
00:47
Now the standard error is the square root of p hat 1 minus p hat divided by n, so that's the square root 0 .28 times 0 .72 divided by 350 or 0 .024.
01:05
That gives us a margin of error of the standard error times z star, so 0 .024 times 2 .5758 is 0 .0618.
01:21
Then we can write that our confidence interval goes from p hat plus the error to p hat minus the error, so 0 .28 plus 0 .024, sorry, plus 0 .0618 gives us 0 .342 to three decimal places, and at the lower end we subtract to get 0 .218 to three decimal places...