1
00:00:00,220 --> 00:00:05,212
If our sample size is 100, that means we now have 99 degrees of freedom instead
2
00:00:05,212 --> 00:00:10,387
of 24. And if we look at our T table, we see that the closest degrees of
3
00:00:10,387 --> 00:00:16,630
freedom to 99 is 100. So we'll just use that one. And again we want .025 in
4
00:00:16,630 --> 00:00:23,171
each tail. Notice that it also says at the bottom Confidence level C. And here
5
00:00:23,171 --> 00:00:28,820
we have 95%. This is the same as how at the top of the column, it has .025% in
6
00:00:28,820 --> 00:00:35,152
either tail. That's equivalent to a 95% confidence interval, pretty cool. And
7
00:00:35,152 --> 00:00:42,592
we see that the t critical value is 1.984 and negative 1.984. Therefore, the
8
00:00:42,592 --> 00:00:51,708
margin of error is 1.984 times s, divided by root n. And this is 39.68. Notice
9
00:00:51,708 --> 00:00:55,677
that now the margin of error got a lot smaller than it was before with a sample
10
00:00:55,677 --> 00:01:03,430
size of 25. Before the margin of error was 2.064 times 200 divided by the
11
00:01:03,430 --> 00:01:10,410
square root of 25, which was 82.56. So when we increase the sample size, we
12
00:01:10,410 --> 00:01:16,256
decrease our margin of error, and we're more precise. And remember, when we
13
00:01:16,256 --> 00:01:21,261
increase the sample size, we also have more degrees of freedom and therefore,
14
00:01:21,261 --> 00:01:28,323
our t distribution goes from wider to skinnier as it approaches normality.