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