So now, we're assuming that this sample mean is one of the 98% that falls within
2.33 standard deviations of the population mean, in this case Mu sub BT. And if
that's the case, then Mu sub BT must be, in turn, within 2.33 standard
deviations of this sample mean. So, the sample mean minus 2.33 standard
deviations, which is 1.01, will be our lower bound for this confidence interval.
So, this comes out to about 37.65, and then our upper bound for the 98%
confidence interval be 40 plus 2.33 times 1.01. So, this is 42.35 approximately.
So basically, we got the sample mean 40, and we decided that it's possible that
it's either here or here on the distribution, such that 1% of the data is either
above it or below it. Before, with the 95% confidence interval, we said most
likely it's going to be a little bit closer to the mean, so that 2.5% of the
data is above it and 2.5% is below. But now, we're being a little more lenient.
We're allowing this sample mean to be a little bit further from the population
mean. And, so now, we have a slightly bigger interval. But now, we're more sure
that the true population mean will be in this interval. Recall that before the
95% confidence interval was from 38.01 to 41.99, so it was a little smaller than
this. Good job.