00:01
So in this question we have a study of a total number n is 109 fatal accidents, where i think that there's a formatting error where numbers get repeated here, so i'm going on that basis, and their distribution is month and number of accidents.
00:30
So we have january, february, march, april, may, june, july, august, september, october, november and december.
00:52
So this is month continued and number of accidents continued.
01:00
So in january we have 8 and 7, 6, 6, 8, 10, 6, 18, 11, 6, 6 and 17.
01:17
So what are the null and alternate hypothesis? well the claim is that the number of fatal accidents doesn't vary from month to month, and actually in a chi -squared test a claim that posits a particular distribution is the null hypothesis.
01:45
So one, our null hypothesis is that the number of accidents doesn't vary, and our alternate hypothesis is going to be that the number of accidents does vary.
02:05
So step two, the null hypothesis tells us that the proportion for month i is just 1 over the number of months, which is 1 12, because it's constant each time, so and they're all equal.
02:28
So that means that we can state our proportions as h0, pi equals 1 12 for i equals 1 to 12, and the alternate hypothesis is that pi is not equal to 1 12 for at least one i.
02:49
Now part four, we want to find the expected values for the number of fatal accidents that occurred in january.
02:56
So the expected number for january is just going to be the number in total times p january, which is the total number divided by 12.
03:11
So that's 109 over 12, and we round to two decimal places to get 9 .08.
03:21
Part five, the same for september.
03:25
So the expected number for september is going to be exactly the same, n total times psep, which is n total over 12, which is 9 .08, and in fact it's going to be 9 .08 for every month...