[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.22,0:00:05.21,Default,,0000,0000,0000,,If our sample size is 100, that means we now have 99 degrees of freedom instead
Dialogue: 0,0:00:05.21,0:00:10.39,Default,,0000,0000,0000,,of 24. And if we look at our T table, we see that the closest degrees of
Dialogue: 0,0:00:10.39,0:00:16.63,Default,,0000,0000,0000,,freedom to 99 is 100. So we'll just use that one. And again we want .025 in
Dialogue: 0,0:00:16.63,0:00:23.17,Default,,0000,0000,0000,,each tail. Notice that it also says at the bottom Confidence level C. And here
Dialogue: 0,0:00:23.17,0:00:28.82,Default,,0000,0000,0000,,we have 95%. This is the same as how at the top of the column, it has .025% in
Dialogue: 0,0:00:28.82,0:00:35.15,Default,,0000,0000,0000,,either tail. That's equivalent to a 95% confidence interval, pretty cool. And
Dialogue: 0,0:00:35.15,0:00:42.59,Default,,0000,0000,0000,,we see that the t critical value is 1.984 and negative 1.984. Therefore, the
Dialogue: 0,0:00:42.59,0:00:51.71,Default,,0000,0000,0000,,margin of error is 1.984 times s, divided by root n. And this is 39.68. Notice
Dialogue: 0,0:00:51.71,0:00:55.68,Default,,0000,0000,0000,,that now the margin of error got a lot smaller than it was before with a sample
Dialogue: 0,0:00:55.68,0:01:03.43,Default,,0000,0000,0000,,size of 25. Before the margin of error was 2.064 times 200 divided by the
Dialogue: 0,0:01:03.43,0:01:10.41,Default,,0000,0000,0000,,square root of 25, which was 82.56. So when we increase the sample size, we
Dialogue: 0,0:01:10.41,0:01:16.26,Default,,0000,0000,0000,,decrease our margin of error, and we're more precise. And remember, when we
Dialogue: 0,0:01:16.26,0:01:21.26,Default,,0000,0000,0000,,increase the sample size, we also have more degrees of freedom and therefore,
Dialogue: 0,0:01:21.26,0:01:28.32,Default,,0000,0000,0000,,our t distribution goes from wider to skinnier as it approaches normality.