00:01
So for this problem, i first need to note that i'm fairly certain that there was a mistake in the way that the question was written.
00:09
So we're told that these measurements here are proportions.
00:15
But first of all, we can see that all of those are given as integer values rather than being decimals or rather than fractions.
00:23
Additionally, we know that we're told that there were 25 questions overall, and that the historical average was 71%.
00:44
If these were the proportions, and that's 21%, 15%, 19%, and so on, then, well, we are way, way off from the historical average.
00:54
But if those are actually the number of correct answers out of 25, then the data makes a lot more sense.
01:02
So that is the assumption that i'm going to be working with here, that those are the counts of correct answers.
01:07
So the actual proportions would correspond to, let's see here, one moment, i'm just going to quickly calculate out what the proportions here are, just by taking all of my data points and dividing the whole thing by 25.
01:21
So, yeah, we can see now translating these into decimal values off to the side here.
01:27
These make a lot more sense as being described as proportions.
01:31
So for finding the upper and lower control limits for the appropriate p chart here, we'd have that our sigma value is equal to the square root of p or p hat times one minus p hat over n...