[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.19,0:00:02.66,Default,,0000,0000,0000,,- [Instructor] We are asked\Nwhat is the critical value,
Dialogue: 0,0:00:02.66,0:00:05.79,Default,,0000,0000,0000,,t star or t asterisk, for constructing
Dialogue: 0,0:00:05.79,0:00:09.31,Default,,0000,0000,0000,,a 98% confidence interval for a mean
Dialogue: 0,0:00:09.31,0:00:14.17,Default,,0000,0000,0000,,from a sample size of n is\Nequal to 15 observations?
Dialogue: 0,0:00:14.17,0:00:16.63,Default,,0000,0000,0000,,So just as a reminder\Nof what's going on here,
Dialogue: 0,0:00:16.63,0:00:18.37,Default,,0000,0000,0000,,you have some population.
Dialogue: 0,0:00:18.37,0:00:19.58,Default,,0000,0000,0000,,There's a parameter here,
Dialogue: 0,0:00:19.58,0:00:21.41,Default,,0000,0000,0000,,let's say it's the population mean.
Dialogue: 0,0:00:21.41,0:00:24.97,Default,,0000,0000,0000,,We do not know what this\Nis, so we take a sample.
Dialogue: 0,0:00:24.97,0:00:27.58,Default,,0000,0000,0000,,Here we're going to take a sample of 15,
Dialogue: 0,0:00:27.58,0:00:30.99,Default,,0000,0000,0000,,so n is equal to 15, and from that sample
Dialogue: 0,0:00:30.99,0:00:33.20,Default,,0000,0000,0000,,we can calculate a sample mean.
Dialogue: 0,0:00:33.20,0:00:36.34,Default,,0000,0000,0000,,But we also want to construct\Na 98% confidence interval
Dialogue: 0,0:00:36.34,0:00:38.01,Default,,0000,0000,0000,,about that sample mean.
Dialogue: 0,0:00:38.01,0:00:39.88,Default,,0000,0000,0000,,So we're going to go take that sample mean
Dialogue: 0,0:00:39.88,0:00:42.80,Default,,0000,0000,0000,,and we're going to go plus or\Nminus some margin of error.
Dialogue: 0,0:00:42.80,0:00:44.51,Default,,0000,0000,0000,,Now in other videos we have talked about
Dialogue: 0,0:00:44.51,0:00:46.69,Default,,0000,0000,0000,,that we want to use\Nthe t distribution here
Dialogue: 0,0:00:46.69,0:00:49.85,Default,,0000,0000,0000,,because we don't want to\Nunderestimate the margin of error,
Dialogue: 0,0:00:49.85,0:00:52.66,Default,,0000,0000,0000,,so it's going to be t star times
Dialogue: 0,0:00:52.66,0:00:56.20,Default,,0000,0000,0000,,the sample standard deviation divided by
Dialogue: 0,0:00:56.20,0:00:59.34,Default,,0000,0000,0000,,the square root of our sample\Nsize, which in this case
Dialogue: 0,0:00:59.34,0:01:02.32,Default,,0000,0000,0000,,is going to be 15, so\Nthe square root of n.
Dialogue: 0,0:01:02.32,0:01:03.57,Default,,0000,0000,0000,,What they're asking us is
Dialogue: 0,0:01:03.57,0:01:05.76,Default,,0000,0000,0000,,what is the appropriate critical value?
Dialogue: 0,0:01:05.76,0:01:10.37,Default,,0000,0000,0000,,What is the t star that we\Nshould use in this situation?
Dialogue: 0,0:01:10.37,0:01:13.62,Default,,0000,0000,0000,,We're about to look at, I\Nguess we call it a t table
Dialogue: 0,0:01:13.62,0:01:16.89,Default,,0000,0000,0000,,instead of a z table, but\Nthe key thing to realize
Dialogue: 0,0:01:16.89,0:01:19.67,Default,,0000,0000,0000,,is there's one extra variable\Nto take into consideration
Dialogue: 0,0:01:19.67,0:01:23.09,Default,,0000,0000,0000,,when we're looking up the\Nappropriate critical value
Dialogue: 0,0:01:23.09,0:01:27.34,Default,,0000,0000,0000,,on a t table, and that's this\Nnotion of degree of freedom.
Dialogue: 0,0:01:27.34,0:01:29.67,Default,,0000,0000,0000,,Sometimes it's abbreviated df.
Dialogue: 0,0:01:29.67,0:01:31.97,Default,,0000,0000,0000,,I'm not going in depth\Non degrees of freedom.
Dialogue: 0,0:01:31.97,0:01:34.72,Default,,0000,0000,0000,,It's actually a pretty deep concept,
Dialogue: 0,0:01:34.72,0:01:36.88,Default,,0000,0000,0000,,but it's this idea that you\Nactually have a different
Dialogue: 0,0:01:36.88,0:01:40.67,Default,,0000,0000,0000,,t distribution depending on\Nthe different sample sizes,
Dialogue: 0,0:01:40.67,0:01:42.54,Default,,0000,0000,0000,,depending on the degrees of freedom,
Dialogue: 0,0:01:42.54,0:01:44.99,Default,,0000,0000,0000,,and your degree of freedom is going to be
Dialogue: 0,0:01:44.99,0:01:47.49,Default,,0000,0000,0000,,your sample size minus one.
Dialogue: 0,0:01:47.49,0:01:50.06,Default,,0000,0000,0000,,In this situation, our degree\Nof freedom is going to be
Dialogue: 0,0:01:50.06,0:01:54.10,Default,,0000,0000,0000,,15 minus one, so in this\Nsituation our degree of freedom
Dialogue: 0,0:01:54.10,0:01:56.16,Default,,0000,0000,0000,,is going to be equal to 14.
Dialogue: 0,0:01:56.16,0:01:58.45,Default,,0000,0000,0000,,This isn't the first time\Nthat we have seen this.
Dialogue: 0,0:01:58.45,0:02:00.53,Default,,0000,0000,0000,,We talked a little bit\Nabout degrees of freedom
Dialogue: 0,0:02:00.53,0:02:03.47,Default,,0000,0000,0000,,when we first talked about\Nsample standard deviations
Dialogue: 0,0:02:03.47,0:02:05.21,Default,,0000,0000,0000,,and how to have an unbiased estimate
Dialogue: 0,0:02:05.21,0:02:07.39,Default,,0000,0000,0000,,for the population standard deviation.
Dialogue: 0,0:02:07.39,0:02:09.84,Default,,0000,0000,0000,,In future videos we'll go into\Nmore advanced conversations
Dialogue: 0,0:02:09.84,0:02:12.08,Default,,0000,0000,0000,,about degrees of freedom,\Nbut for the purposes
Dialogue: 0,0:02:12.08,0:02:14.64,Default,,0000,0000,0000,,of this example, you need to know that
Dialogue: 0,0:02:14.64,0:02:17.38,Default,,0000,0000,0000,,when you're looking at the t distribution
Dialogue: 0,0:02:17.38,0:02:19.64,Default,,0000,0000,0000,,for a given degree of freedom,\Nyour degree of freedom
Dialogue: 0,0:02:19.64,0:02:21.49,Default,,0000,0000,0000,,is based on the sample\Nsize and it's going to be
Dialogue: 0,0:02:21.49,0:02:23.76,Default,,0000,0000,0000,,your sample size minus one\Nwhen we're thinking about
Dialogue: 0,0:02:23.76,0:02:26.28,Default,,0000,0000,0000,,a confidence interval for your mean.
Dialogue: 0,0:02:26.28,0:02:29.08,Default,,0000,0000,0000,,Now let's look at the t table.
Dialogue: 0,0:02:29.08,0:02:32.00,Default,,0000,0000,0000,,We want a 98% confidence interval
Dialogue: 0,0:02:32.00,0:02:35.89,Default,,0000,0000,0000,,and we want a degree of freedom of 14.
Dialogue: 0,0:02:36.89,0:02:40.01,Default,,0000,0000,0000,,Let's get our t table out, and I actually
Dialogue: 0,0:02:40.01,0:02:41.94,Default,,0000,0000,0000,,copied and pasted this\Nbottom part and moved it up
Dialogue: 0,0:02:41.94,0:02:43.65,Default,,0000,0000,0000,,so you could see the whole thing here.
Dialogue: 0,0:02:43.65,0:02:45.30,Default,,0000,0000,0000,,What's useful about this t table
Dialogue: 0,0:02:45.30,0:02:47.30,Default,,0000,0000,0000,,is they actually give\Nour confidence levels
Dialogue: 0,0:02:47.30,0:02:50.45,Default,,0000,0000,0000,,right over here, so if you\Nwant a confidence level of 98%,
Dialogue: 0,0:02:50.45,0:02:53.02,Default,,0000,0000,0000,,you're going to look at this column,
Dialogue: 0,0:02:53.02,0:02:55.58,Default,,0000,0000,0000,,you're going to look at\Nthis column right over here.
Dialogue: 0,0:02:55.58,0:02:59.16,Default,,0000,0000,0000,,Another way of thinking about\Na confidence level of 98%,
Dialogue: 0,0:02:59.16,0:03:02.62,Default,,0000,0000,0000,,if you have a confidence level of 98%,
Dialogue: 0,0:03:02.62,0:03:07.23,Default,,0000,0000,0000,,that means you're leaving 1% unfilled in
Dialogue: 0,0:03:07.23,0:03:09.68,Default,,0000,0000,0000,,at either end of the\Ntail, so if you're looking
Dialogue: 0,0:03:09.68,0:03:12.78,Default,,0000,0000,0000,,at your t distribution,\Neverything up to and including
Dialogue: 0,0:03:12.78,0:03:16.62,Default,,0000,0000,0000,,that top 1%, you would\Nlook for a tail probability
Dialogue: 0,0:03:16.62,0:03:21.45,Default,,0000,0000,0000,,of 0.01, which is, you\Ncan't see right over there.
Dialogue: 0,0:03:21.45,0:03:23.04,Default,,0000,0000,0000,,Let me do it in a slightly brighter color,
Dialogue: 0,0:03:23.04,0:03:25.82,Default,,0000,0000,0000,,which would be that tail\Nprobability to the right.
Dialogue: 0,0:03:25.82,0:03:27.65,Default,,0000,0000,0000,,Either way, we're in this\Ncolumn right over here.
Dialogue: 0,0:03:27.65,0:03:30.08,Default,,0000,0000,0000,,We have a confidence level of 98%.
Dialogue: 0,0:03:30.08,0:03:32.33,Default,,0000,0000,0000,,Remember, our degrees of freedom,
Dialogue: 0,0:03:32.33,0:03:37.19,Default,,0000,0000,0000,,our degree of freedom here,\Nwe have 14 degrees of freedom,
Dialogue: 0,0:03:37.19,0:03:41.61,Default,,0000,0000,0000,,so we'll look at this row right over here.
Dialogue: 0,0:03:41.61,0:03:43.21,Default,,0000,0000,0000,,So there you have it.
Dialogue: 0,0:03:43.21,0:03:46.33,Default,,0000,0000,0000,,This is our critical t value, 2.624.
Dialogue: 0,0:03:48.75,0:03:51.20,Default,,0000,0000,0000,,So let's just go back here.
Dialogue: 0,0:03:51.20,0:03:56.20,Default,,0000,0000,0000,,2.264 is this choice right\Nover here, and we're done.