00:01
Once again, we have a new problem, and here we're dealing with populations.
00:07
Remember, if you have a population, you could get the values of the average of the population, say it's something like average income.
00:22
So this would be mew, would be the average population, and then within the population, you'd pick up a sample and also have the average population.
00:33
The sample means, so x bar is the sample mean, and then mu is the population mean, and you can hypothesize a nal, nal means no difference, so no difference between your mean value and the hypothesized mean.
00:59
Another way of doing the now would be saying mu is great to the value.
01:04
Than or equal to mu not or mu is less than or equal to mu not.
01:10
The alternative hypothesis would be the opposites of all of these.
01:16
So you'd have mu is not equal to mu not or mu is if this one is hypothesized as greater than, the alternative would be hypothesized as less than and then the opposite is also true.
01:32
So, for example, you wanted to test if the average income of the state of nevada, for example, was $60 ,000.
01:43
You hypothesized that.
01:45
And then you have a couple, a household that makes an average of, say, or maybe you take a sample, a bunch of households, families, and then sample them out and see that the average ends up being maybe $70 ,000.
02:04
So you want to test to see if your hypothesis makes sense that the average income, household income, or the median household income in the state of nevada is $70 ,000.
02:18
So that's what's going to happen when you're running a hypothesis testing for inferential statistics.
02:24
So in this particular problem, we have 15 large cities in the u .s.
02:31
Or u .s.
02:31
Or u .s.
02:31
Us cities.
02:33
We have 15 of them, 15 large cities, and the average commute time is 25 .4 minutes for the residents of these cities.
02:49
And we also have austin, texas, with an average commute time of 22 .1 minute, one minutes.
03:02
If you want to call it that, and then the standard deviation is the same as 5 .3 minutes.
03:10
So our goal in this problem is to hypothesize that the to test if the commute time in austin, texas is significantly less.
03:35
Is significantly less than the 15 series.
03:43
So that's what we wanna test.
03:45
So in this particular problem, we'll first of all come up with a now hypothesis.
03:52
If we're testing to see if it's significantly less, it means the now hypothesis will be testing the opposite, which is greater than or equal to 25 .4 minutes.
04:04
The alternative hypothesis, which is our claim, this is the claim we're making that our sample is significantly less than 25 .4, which is a commute time.
04:19
That's the first thing we're doing.
04:21
And then the second thing is we'll compute a test statistic.
04:31
We'll compute a test statistic.
04:33
So t is x bar minus m u over s over radical n which gives us 22 .1 minus 25 .4 all over 5 .3 over radical 25 and then we end up getting negative 3 .113 that's our t test and so once we we have our t test we can we know sample size n is 25 and then the degrees of freedom n minus 1 is 24...