00:01
Alright, so we're looking at some data, which is the water rates for 42 n equals 42 randomly selected cities in the united states.
00:13
And we're told that in tulsa, the mean water rate is 21 .62, so $21 .62.
00:20
And what we're going to do is run a little hypothesis test if it's significantly different than the mean of this.
00:29
So our null hypothesis will be that the mean is in fact 21 .62.
00:37
The alternative, which one, is that it's not equal to 21 .62.
00:43
And we're actually going to do a one -tailed test too.
00:46
We'll do two tests as well, the two -tailed as well.
00:50
First, because it's kind of fun to see both as we're learning this stuff.
00:55
You wouldn't do this in practice.
00:57
In the real world, you'd generally have your hypothesis set up ahead of time, but it's good to see how we do both.
01:03
And we're going to use the p -value and critical value approach.
01:06
So we're going to test at the alpha of 0 .05 level of significance, which means that we reject h -naught if our p -value is less than this value.
01:13
We're also going to use the critical value approach, which will be to reject h -naught if the absolute value of our test statistic is greater than the t -critical value, which we will find along the way.
01:23
So because we have a sample size greater than 30, the distribution about our sample means is approximately normal.
01:30
So we can use our t -distribution.
01:33
The formula is x -bar minus the mean, this mean, 21 .62, divided by s over root n.
01:40
N's going to be 42.
01:41
S we'll find in a moment.
01:43
So let's go ahead and find x -bar and s and t.
01:47
All right, so here we go.
01:48
Here's s, the standard deviation of the sample using this spreadsheet formula.
01:52
X -bar using this spreadsheet formula, the average.
01:56
These are the cell references there.
01:59
And the test statistic, when you put everything in to this formula, you get negative 0 .98.
02:04
Good.
02:05
So let's go ahead and do the p -value approach first.
02:09
It's one tail, two tail.
02:13
Again, for right now, we're going to look at just two tail.
02:16
So two tails.
02:17
We use this spreadsheet formula, t -dist, the absolute value of the test score of the test statistic.
02:25
There's the cell reference right there.
02:28
41, this is your degrees of freedom.
02:30
You need your degrees of freedom, which in this case is n minus 1.
02:36
So 42 minus 1 is 41...