00:01
Today we're looking at something called home field advantage, which is something that suggests that in a given sport home teams will beat the away team more often than half the time for a variety of reasons.
00:15
We don't know what those reasons are, but there's some reason why home field home teams have it in terms.
00:20
They're gonna win more than half the time.
00:21
So that's gonna be our null hypothesis that the mean proportion or the true population proportion, i should say, is greater than, is equal to a half.
00:29
That's null.
00:30
We're gonna assume that there is no benefit to being at home.
00:34
The alternative is that there is a benefit, that the proportion is actually greater than 0 .5 for the probability of winning, the proportion of wins for home teams is actually greater than that.
00:48
And there was a thousand randomly selected nfl games, and of them 574 had the home team win.
00:58
And we're gonna do a one proportion z test for this, and in order for that to be the case, in order for us to do that we need to check some of the criteria that n times p is greater than equal to 10 and indeed it is we're going to say p is 0 .5 so 1000 times 0 .5 is 500 greater than 10 likewise n times 1 minus p needs to be bigger than or equal to 10 and indeed a thousand times 1 minus 0 .5 is also bigger than 10 so that works so we need to we're going to do one portion z test so our z score is the p hat is found by taking our proportion estimate minus our population proportion that we're assuming to be 0 .5 divided by the square root of p times minus p all over n which is the sample size of a thousand so we need p hat p hat is found by taking x over n so that's 0 .574 over 1000 oops i jumped ahead it's 574 divided by a thousand which is 0 .574.
01:59
So plug this into our formula.
02:01
0 .574 minus 0 .5 all over the square root of a half times a half, which is 1 minus 0 .5 divided by a thousand.
02:16
And we'll get a z -score of 4 .68.
02:21
Little side note, this square root term in the denominator is also called the standard error.
02:26
Let's see this sigma sub p.
02:29
And mu sub p is another way of showing the population proportion that we're assuming to be.
02:32
So 0 .5, you might see this p or u sub p.
02:37
Actually this would be p hats.
02:43
All right, and the z -score is 4 .68.
02:49
Now what this means is we've transformed this into a z -score, our population proportion estimate of p -hat, which is 0 .574, into a z -score, which has ascended around 0.
03:02
We found a z -score of 4 .68.
03:05
And this black area here, this is called our p -value.
03:10
And for our test, we are testing it at the alpha of 0 .02 level of significance.
03:17
And if our p -value is less than the alpha, we reject our hypothesis.
03:23
And we need to find that p -value.
03:25
And i use my spreadsheet to do that.
03:27
You could look it up in my textbook as well...