﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.33,0:00:07.61,Default,,0000,0000,0000,,So now, we're assuming that this sample mean is one of the 98% that falls within Dialogue: 0,0:00:07.61,0:00:14.94,Default,,0000,0000,0000,,2.33 standard deviations of the population mean, in this case Mu sub BT. And if Dialogue: 0,0:00:14.94,0:00:20.98,Default,,0000,0000,0000,,that's the case, then Mu sub BT must be, in turn, within 2.33 standard Dialogue: 0,0:00:20.98,0:00:27.62,Default,,0000,0000,0000,,deviations of this sample mean. So, the sample mean minus 2.33 standard Dialogue: 0,0:00:27.62,0:00:35.39,Default,,0000,0000,0000,,deviations, which is 1.01, will be our lower bound for this confidence interval. Dialogue: 0,0:00:35.39,0:00:42.70,Default,,0000,0000,0000,,So, this comes out to about 37.65, and then our upper bound for the 98% Dialogue: 0,0:00:42.70,0:00:51.72,Default,,0000,0000,0000,,confidence interval be 40 plus 2.33 times 1.01. So, this is 42.35 approximately. Dialogue: 0,0:00:51.72,0:00:57.12,Default,,0000,0000,0000,,So basically, we got the sample mean 40, and we decided that it's possible that Dialogue: 0,0:00:57.12,0:01:02.51,Default,,0000,0000,0000,,it's either here or here on the distribution, such that 1% of the data is either Dialogue: 0,0:01:02.51,0:01:08.66,Default,,0000,0000,0000,,above it or below it. Before, with the 95% confidence interval, we said most Dialogue: 0,0:01:08.66,0:01:14.72,Default,,0000,0000,0000,,likely it's going to be a little bit closer to the mean, so that 2.5% of the Dialogue: 0,0:01:14.72,0:01:20.36,Default,,0000,0000,0000,,data is above it and 2.5% is below. But now, we're being a little more lenient. Dialogue: 0,0:01:20.36,0:01:26.02,Default,,0000,0000,0000,,We're allowing this sample mean to be a little bit further from the population Dialogue: 0,0:01:26.02,0:01:31.82,Default,,0000,0000,0000,,mean. And, so now, we have a slightly bigger interval. But now, we're more sure Dialogue: 0,0:01:31.82,0:01:37.99,Default,,0000,0000,0000,,that the true population mean will be in this interval. Recall that before the Dialogue: 0,0:01:37.99,0:01:44.78,Default,,0000,0000,0000,,95% confidence interval was from 38.01 to 41.99, so it was a little smaller than Dialogue: 0,0:01:44.78,0:01:46.81,Default,,0000,0000,0000,,this. Good job.