00:01
So your first question is to find a 99 % confidence interval for a proportion.
00:09
And so we're going to take what we got, which is a 39 out of 50, or that is 0 .78, plus or minus, and we use the 2 .576, and then we will have our 0 .78 times with complement, 0 .22, divided by the sample size of 50.
00:29
And when all is said and done, when we do our calculations, we get 0 .629 to 0 .931.
00:40
So we are 99 % confident that the actual proportion lies somewhere in here, relatively wide, because that sample size isn't huge.
00:49
Now, the third question, you had two parts, and we had to first of all find a 95 % confidence interval for the mean.
01:00
And so we are going to take the mean, and we're going to find a z interval because we're told the population standard deviation is 8 .3 and whatever the unit of measure is.
01:11
So we're going to take our 92, that was our x bar, plus or minus, and the z value is 1 .96 for a 95 % confidence interval with a z value.
01:23
And then we take our sample, excuse me, our population standard deviation divided by the square root of n, and n was 80%.
01:31
And so that yields an interval that is from 90 .27 to 93 .73.
01:41
And then in part b, you wanted to do a hypothesis test to see if there is a difference.
01:49
And you asked, i guess the first part of the question was, is this a one or a two -tailed test? and it's going to be a two -tailed test because you just want to see if there's a change.
01:58
Your null will be that the mean is 90, and then the alternate hypothesis is that the mean is not 90.
02:07
And because of just wanting to not, not knowing whether you were looking to see if the change is higher or lower, that's going to make it be a two -tailed test.
02:18
And so now we need to determine our tests.
02:21
So we are having, we truthfully could use this confidence interval, your l .e.
02:28
Level you're using is 0 .05...