00:01
Once again, welcome to a new problem.
00:05
This time we're dealing with inferential statistics.
00:09
Inferential statistics and when you think about inferential statistics, the two types of data that you're going to be dealing with when it comes to inferential statistics.
00:23
So you have numerical data and you also have categorical types of data.
00:30
So when the independent variable, which is typically the x variable and the dependent variable, when these two variables are both categorical, then you have the kye square test for independence that's appropriate for this type of distribution.
00:58
So you have the kye square test for independence, or for independence, that's appropriate for this type of distribution.
01:03
That happens to be appropriate for this type of distribution.
01:08
So the kye square distribution is right tails where you have the kai critical value and that's compared to the kai square test statistic, which for example if this was my kai square test statistic then what's going to happen is that the portion that's holding on the right that's going to be my p value and if my p value is less than alpha and alpha of 05 so i reject the now hypothesis and what it comes to kai square test for typical test the now hypothesis is that the the now hypothesis is that the distributions are similar to say underlying distributions.
02:19
Or you could also say that the distributions are different.
02:29
When it comes to kyrsquare test for relationship, there is no relationship between the explanatory and the response variable and then also on the other side you'd have that there is a relationship between these two variables the dependent and the dependent the kai square test statistic involves the summation of the observed values those are the given values minus the expected values these are the expected values and these are expected of predicted values and these are expected values and then you divide by the expected values if i wanted to say compute a typical expected value for the most part you're going to take the row total times the column total over the ground total and by that we mean that if i have a, b, c, and d.
03:46
This is the summation of a, b, summation of c d.
03:53
And this one is summation of b d, summation of ac, and this is the grand total.
04:03
So the row total, for example, if i want to get the expected value for this portion, i would take the row total times the column total divided by the grand total so for the most part that's how you run the kaly square test coming back to our problem we have a table with a special table and this table is going to have you know different times these tables is going to have different times and we'll talk about it is 6 so we have the time right here for 5 to 559 p .m.
05:02
That's the time right there and this is day one we also have information about day 2 and we'll talk about the meaning of this information we also have day 3 we also have day 4 we have the 4th day and we have day five we also have day six and we have day seven and then this column we have the average and then of course we're going to have the proportion and these are the times that you're saying we have six to six fifty nine seven to seven fifty nine eight to eight fifty nine to nine ten to 1069 and then we have 11 to 11 .59 and these are the times of the date that we have and then we're going to have the numbers that are relevant to the problem.
06:32
So we have 15, 30, 36, 29, 21, 12, we have 8, 19, 239, 23, 19, 23, 29, 23, 12, we have 8, 19, 23, 23, twenty twelve seven and twenty one and twenty four that's thirty nine we have twenty twelve fifteen we have nine we have twenty five thirty five twenty nine of nineteen we have twelve we have twenty eight thirty nine there's twenty four we have eighteen we have 10, we have 12, now we have 15, we have 29, 30, 32, 14, we have 15, we have 12, 16, we have 26, 27, 20, 20, 14, of 9, and then in terms of the averages, we have 16 .7 and 4, we're going to get that right, 16 .7 ,1, we have 26 .7, 1, we have 26, point four three we have 34 .2 .9 we have 28 .14, we have 17 .7 million.
08:26
We also have i think this kicked one, 16 and then 2014, 19, 1626.
09:07
This is 32.
09:10
This is 27, 20, i think i want to change these ones.
09:19
And then we have 1526 32 27 20 14 and 9 yeah that's what we have and then these numbers we have 34 .29 28 .14 and then for 20 17 17 17000 of 12 .86 and then 12 .86 and down for get 1957 the last column for the proportions 0 .15.
10:03
0 .181, 0 .235, we have 0 .193, 0 .101080, 0 .086.
10:24
So we do have a table right here and we want to talk about the contents of the table.
10:33
So this is a restaurant, this is a restaurant owner, and the goal, the goal is to determine the demand, the peak demand periods.
11:01
So we want to see what the peak demand periods is.
11:04
And this is based on the hours of operation.
11:08
This is based on the hours of operation.
11:12
And this is going to help with serving customers.
11:19
It's going to help with serving customers.
11:25
He assumes that 60 % of daily customers typically show up between the hours of 6 p .m.
11:40
And 8 .59 p .m.
11:43
With equal distribution, equal distribution during the times.
11:54
And then also 40 % of the customers come at other times, come at other times, also with equal distributions.
12:15
So they come at other times.
12:20
The given data represents the distribution so the given data to see if the observed the observed distribution is similar to the expected distribution or it's different.
13:20
It's different and we want to determine the p value for the test.
13:28
We also want to see what the p value for the test is.
13:32
In this instant, the knowledge there's more difference in distributions and then the alternative is there's a difference in distributions.
13:53
So this is based off of what they have hypothesized and we want to see if these distributions do line up.
14:02
So we have the data presented.
14:07
We have the data presented...