00:01
So i'm guessing that this is the full problem that you were given, where we have 432 people, 108 had sleep apnea.
00:10
So to find the point estimate, that first part of the problem, the point estimate is simply going to be the number who had sleep apnea, 108, divided by the sample size, 432, which happens to come out to exactly 1 over 4 or 0 .25.
00:26
Then that second part of the problem, we're asked for a 99 % confidence interval.
00:33
Now, for the 99 % confidence interval, i'll first note that our z of alpha over 2 is going to be equal to this value we have here, 2 .32635, and our formula for our 99 % confidence interval will be as shown here in just a moment.
00:56
So we have that the true population proportion is going to be somewhere between the measured or the estimate plus or minus z alpha times root p prime, q prime over n.
01:08
So that's that p prime is the measured population proportion and q prime would be one minus the measured population proportion.
01:16
So we'd have that the lower end of our confidence interval is going to be given by 0 .25 minus 2 .32635 times the square root.
01:26
Root of 0 .25 times, as i said, our q prime is 1 minus 0 .25, which is 0 .75...