00:01
All righty, so we're looking at blood glucose levels.
00:05
And if a patient has an average of 100 milligrams per deciliter, that would indicate good control.
00:12
And if the average is below 100, that's even better.
00:15
And so a particular patient, towards the last 100 blood glucose levels, so n is 100.
00:22
Oh, and the population mean is also 100.
00:26
And we're told that right here, this is our population mean right here.
00:31
So mu.
00:32
This is our n.
00:35
And this one patient found that the mean of those 100 samples was 85, so that's x bar.
00:49
And we know the population standard deviation is 20.
00:52
So that's sig pop.
00:53
So that is sigma, not s, because it's the population to indivation at sigma.
01:01
And we're being asked if this is compelling statistical evidence that the patient has a mean blood the glucose level below 100.
01:11
So let's say our hypotheses that the mean is greater than equal to 100.
01:20
And the alternative is that the mean is less than 100 for this particular person.
01:32
And we will reject h0 if the p value we find is less than the alpha of 0 .05.
01:48
And we're told that 0 .05 right here.
01:50
So we are going to use, get our z score for the sampling distribution.
02:00
And that formula is given as x bar minus mu sub x bar, divided by sigma sub x bar.
02:09
And this is called this standard error.
02:13
And the actual calculation for that is sigma over root n.
02:18
That whole thing's in the denominator.
02:20
Oh, and just to note this piece here, this sigma sub x bar, that's the same thing as mu.
02:29
Or mu said x -b, that's the same as mute.
02:30
That's the population mean.
02:34
So let's do our calculations...