00:01
All right, so the first thing that i'll note here is that we are given, we are originally given that our sample size, n is equal to 40.
00:10
We're given that our sample mean is equal to 50.
00:15
Oops, 50 .575.
00:21
And the sample standard deviation, s equals 1 .6 -438.
00:26
Knowing that then, what we can do is generate our confidence interval here using, for instance, a tia -84 calculator.
00:38
We can do second, or actually, pardon me, we don't want to do second.
00:43
We want to do stat, go to calc, or actually, pardon me, we want to go to tests, rather.
00:49
Scroll down, and we want t -interval.
00:52
Now i'll input the statistics.
00:55
We have x bar is 50 .575.
01:00
Sx, that's the standard deviation of x bar.
01:03
That's going to be the sample standard deviation, 1 .6 -438, divided by the square root of our sample size.
01:11
So we divide that by the square root of 40.
01:15
And we have that our n value here is equal to 40.
01:20
And we're looking for a 95 % confidence level.
01:25
So c level is 0 .95, or 95 % confidence interval, that is.
01:32
So we calculate this out, and we find that for part a, that interval will be from 50 .492 up to 50 .658.
01:50
So we can note that the lower bound of our confidence interval, 50 .492 is greater than 50.
02:00
So we can be confident and be confident that mu, the population mean value, is at least 50 based on that confidence interval.
02:14
Then, for part b, let's see here...