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