00:01
In this problem, we are trying to test a claim that because many births are induced or involve cesarean section, they are scheduled for other days than saturdays and sundays.
01:01
So because of that, births do not occur on the seven different days of the week with each.
01:34
Equal frequency.
01:45
So if we're going to test that claim, we have to write a null hypothesis and an alternative hypothesis.
01:54
Our null hypothesis is going to be that births do appear or occur on the seven different days of the week with equal frequency.
02:27
And the alternative will be that births do not occur on the seven different days with equal frequency.
03:06
So in essence, our claim is really the alternative hypothesis.
03:15
So we needed to gather and look at the data.
03:19
So you needed to go to appendix b and gather the data that was used to run this test.
03:27
And the data was broken down based on admittance to the hospital.
03:34
And if you looked at how many moms, or soon -to -be moms, were admitted on sundays in that data set, you would find 53.
03:46
On mondays, there were 52.
03:49
On tuesdays, there were 66.
03:53
On wednesdays, there were 72.
03:56
On thursdays there were 57.
04:02
On fridays there were 57 moms to be admitted.
04:06
And on saturdays, there were 43.
04:13
In this particular data set, we looked at 400 admittance to the hospital for birth of a baby.
04:25
Now, if our no hypothesis was going to be true, then that 400, births would be divided evenly over the seven days.
04:37
So if i were to take 400 and divide it by seven, i will end up with 57 and one -seventh for each of those days.
04:57
And i found it easier to leave it as one -seventh rather than as a decimal.
05:05
So what you have here are the observed and the expected frequencies.
05:14
So the top line is our observed and the bottom line is our expected frequency.
05:20
So what we want to do is we want to run a goodness of fit test to see if the actual data, the observed data, fits what is expected.
05:38
And in order to do so, we will have to first calculate the kai square test statistic.
05:50
And to do that, we will apply the formula the sum of observed minus expected quantity squared divided by expected.
06:02
And the fastest way to arrive at that value is to put your data into a graphing calculator.
06:11
So here's my graphing calculator.
06:13
I'm going to hit stat and edit.
06:16
And as you can see, my observed data is in list one.
06:21
And my expected data is in list 2.
06:25
So 57 and 17th translates into 57 .142857.
06:33
So to find the kai square test statistic, i'm going to sit up on top of list 3, and i'm going to have the calculator, take all the values from list 1, all the observed values, subtract their corresponding expected values that are found in list 2, square that deviation before dividing by the expected values in list 2.
07:01
And you're going to get the following decimals.
07:03
And for the sake of recording the information, i'm going to go to three decimal places.
07:09
For sunday, the value would be 0 .30.
07:13
For monday, 0 .463.
07:18
For tuesday, 1 .373.
07:25
For wednesday, 3 .863.
07:31
For thursday, it's going to be 0 .000357.
07:41
For friday, it's going to be the same.
07:44
0 .000357.
07:49
And for saturday, it's going to be the same.
07:52
0 .50 .00.
07:56
So for me to calculate the kai square test statistic, i need to add up those values.
08:08
Again, those values are going to be the o minus e quantity squared divided by e values.
08:16
And if i go back to my graph and calculator where the data is already in, i can quit from the list and say, second stat sum up everything that's in list three.
08:31
And i'm going to get a kai square test statistic of 9 .5.
08:42
The next phase of the hypothesis test is to calculate the p value.
08:52
To calculate our p value, we are actually finding the probability that kai square is greater than that test statistic.
09:05
So to kind of get our bearings on what that means, it's best if we were to draw a kye square distribution.
09:15
And kye square distributions are skewed right graphs, and the shape of those graphs are dependent on the degrees of freedom.
09:24
And degrees of freedom can be found by taking k minus one, and k represents the number of categories that you have separated your data into.
09:34
And if we go back to our chart, we can see that we've separated our data according to the days of the week.
09:42
So there were seven different categories for our data.
09:48
So our degrees of freedom would be six.
09:52
Now, not only does the degrees of freedom give us the shape of the graph, but the degrees of freedom also indicates to us what the mean of the graph is...