00:01
For this problem, let's begin by just gathering up all of our information.
00:04
So for the first group, those assigned to take the drug, we have 150 participants.
00:12
And for the placebo group, we also have 150 participants.
00:20
For the drug group, the mean reduction of blood sugar levels is 25 points with a standard deviation of 3 .1, where i'm noting i'm using sigma here because we are told to assume that the standard deviations are true for the entire population, not just for the sample.
00:42
And then for those who are taking the placebo, their mean reduction is 18 points with a standard deviation of 2 .8.
00:54
And we are asked to calculate 90 % confidence intervals to determine whether there is evidence that the new drug is working.
01:02
So we want to check, do the intervals overlap or not? if the intervals overlap, then that means that the drug does not appear to be working.
01:15
If the intervals do not overlap, then that means that there is a significant difference.
01:20
So when we calculate a 90 % confidence interval with this amount of information, we take the sample mean plus or minus the z -score for a one -tail proportion of 0 .05, times the population standard deviation over the square root of the sample size, where that critical z -score here, i just have this memorized, but you can double check this on a table or with a graphing calculator, that z -score is going to be 1 .645.
01:46
And we can see up here, 90 % confidence, it might be a little bit small, but yeah, rounding to three decimal places.
01:52
For 90 % confidence, the z -score is roughly 1 .645...