WEBVTT
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If our sample size is 100, that means we now have 99 degrees of freedom instead
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of 24. And if we look at our T table, we see that the closest degrees of
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freedom to 99 is 100. So we'll just use that one. And again we want .025 in
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each tail. Notice that it also says at the bottom Confidence level C. And here
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we have 95%. This is the same as how at the top of the column, it has .025% in
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either tail. That's equivalent to a 95% confidence interval, pretty cool. And
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we see that the t critical value is 1.984 and negative 1.984. Therefore, the
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margin of error is 1.984 times s, divided by root n. And this is 39.68. Notice
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that now the margin of error got a lot smaller than it was before with a sample
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size of 25. Before the margin of error was 2.064 times 200 divided by the
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square root of 25, which was 82.56. So when we increase the sample size, we
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decrease our margin of error, and we're more precise. And remember, when we
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increase the sample size, we also have more degrees of freedom and therefore,
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our t distribution goes from wider to skinnier as it approaches normality.