Goodness Fit Tests

Question 1

What are these designed ti din

Answer 1

Using chi 2 tests ti see if data can follow a normal, binomial or passion disturb turn

Question 2

How to use chi 2 test to check if claim is true or not

Answer 2

Use expected as obvious, so if dice Privileg is 1/6

Find chi 2 and use degree of freedom as one row only

Check vs,he and come to conclusion

Question 3

How to do uniform distribution test null hypotthissn

Answer 3

Null is assuming it is fair
Akthernwtive issome alteration

Then reject or accept

Question 4

Okay for passion distribution how to start

Answer 4

Youregonna need to expected frewuencies
Work this out by multiply n by expected pros Iltises

Porbsioty worked out using poison distribution where r starts from 0

Question 5

But what if they don’t give lambda? How can figure it out

Answer 5

The mean is the expected value, so estimate lambda by finding MEAN

Question 6

Now what about the last value on tsble, if it’s 6 + etc, how can you work it out

Answer 6

Remember p(x)= 6+ is the same as 1- p (x) being less than equal to 5
- find this using calculator, but go on POISSON DISTRIBUTION THIS TIME, and CD because tiscumulative

Question 7

Now again must check if any EXPECTED FREWUENCY USING POISSON is less than 5, and if it is thrn?

Answer 7

COMBINE BOTH GROUPS, there and then no need to readjust bevaude only one row, combine the expected frequencies and the group and move on

Question 8

How to calculate degrees of freedom for POISSON?

Answer 8

Basically after combined groups, minus @ like normal and minus 1 again for any PREDICTED PARAMTERS

So if 7 now 6, -1,-1 again for lambda and it beocmes 4!

Question 9

What is null and alternative hypothesis for position distribution test

Answer 9

H0 : x can be modelled by a POISSON distribution
H1: csn’t be muddled

Question 10

So how can we do whole POISSON disturb thing tedt

Answer 10

First need ti find the chi 2 statistic using poisssion modelling
- expected frewuency is now possion formula x n , where r starts from 0
- use Lambadas mean if not given as an estimate . Thid idbevaude the expected value in position is the mean
- now check if any less than 5, if so Cl bine

H0: it can be modelled
H1: it can’t

Critical value at degrees of freedom as columns -1 -1 for parameter predicted

Check
If lower font reject if higher rejcet

Question 11

But BIG IMPORTSNT THING TO REMEMBER ABOUT YOUR LAST PORBSBILKTY, do you just make it 4?

Answer 11

NO POISSON dksturbtiin keeps on going , so must be probability of 4 and above, so use position cd to find 1- 3 and below

AND MULTIPLY BY N AGAIN AS THIS IS JUST PROBBILITY NOT EXOECTED FREAUENCY

Question 12

An easier way to calculate the expected frequencies hack?

Answer 12

Calculate for 0 as normal using the formula. You’ll find its just e to the power of - lambda as 0 cancels those out . Make sure to multiply by 80

2) now multiply by lambda /r Esch time
3) eventually when you get to last one , use poisson cd to find probability and multiply by total remember !

Question 13

Remember if they give you w lambda value by saying mean , what not to do for degree of freedom

Answer 13

DONT SUBTRSVT AGAIN

Question 14

What supports possion model

Answer 14

If the variance and ,wan are the same

Question 15

Finally if your chi sqaured is very low what can this mean

Answer 15

Data was rigged to fit model, fske