1
00:00:00,330 --> 00:00:07,610
So now, we're assuming that this sample mean is one of the 98% that falls within
2
00:00:07,610 --> 00:00:14,940
2.33 standard deviations of the population mean, in this case Mu sub BT. And if
3
00:00:14,940 --> 00:00:20,982
that's the case, then Mu sub BT must be, in turn, within 2.33 standard
4
00:00:20,982 --> 00:00:27,619
deviations of this sample mean. So, the sample mean minus 2.33 standard
5
00:00:27,619 --> 00:00:35,387
deviations, which is 1.01, will be our lower bound for this confidence interval.
6
00:00:35,388 --> 00:00:42,696
So, this comes out to about 37.65, and then our upper bound for the 98%
7
00:00:42,696 --> 00:00:51,717
confidence interval be 40 plus 2.33 times 1.01. So, this is 42.35 approximately.
8
00:00:51,717 --> 00:00:57,115
So basically, we got the sample mean 40, and we decided that it's possible that
9
00:00:57,115 --> 00:01:02,510
it's either here or here on the distribution, such that 1% of the data is either
10
00:01:02,510 --> 00:01:08,662
above it or below it. Before, with the 95% confidence interval, we said most
11
00:01:08,662 --> 00:01:14,722
likely it's going to be a little bit closer to the mean, so that 2.5% of the
12
00:01:14,722 --> 00:01:20,360
data is above it and 2.5% is below. But now, we're being a little more lenient.
13
00:01:20,361 --> 00:01:26,025
We're allowing this sample mean to be a little bit further from the population
14
00:01:26,025 --> 00:01:31,820
mean. And, so now, we have a slightly bigger interval. But now, we're more sure
15
00:01:31,820 --> 00:01:37,987
that the true population mean will be in this interval. Recall that before the
16
00:01:37,987 --> 00:01:44,785
95% confidence interval was from 38.01 to 41.99, so it was a little smaller than
17
00:01:44,785 --> 00:01:46,813
this. Good job.