Chapter 11.2 Flashcards
What is a goodness-to-fit test?
used to test the hypothesis that an observed frequency distribution fits some claimed distribution, test the hypothesis that the population of all outcomes occur with equal frequencies
-requirements:
1) data is randomly selected
2) sample data consist of frequency counts for each of the diff categories
3) for each category, the expected frequency is at least 5
pg. 574
How do you find expected frequencies when they are all ecpected to be all equal?
E=n/k
n is the number of data values
k is the number of categories
don’t have to be whole numbers
total trials/total categories or the average of the outcomes
pg. 576
What is the terminology for goodness-of-fit tests?
O=the observed frequency for a category
E=the expected frequency for a category
p=probability for a category
k=number of categories
n=number of observed sample values
pg. 576
How do you do a goodness-to-fit test by hand?
x^2=Sumation(O-E)^2/E
O=observed frequency
E=expected frequency
use a chart and go step by step for each category
e.g.
O:E:O-E:(O-E)^2:(O-E)^2/E…then add all (O-E)^2/E values togther to find x^2
pg. 577
How do you find the degrees of freedom?
df=k-1
k=number of categories
pg. 578
How to find x^2 with a TI-84
observed freq-L1
expected freq-L2
Stat->test
x^2 GOF-test
k-1 for df
calculate
will give x^2 and P-value
pg. 579
How do you find the P-value from the x^2?
x^2cdf(x^2 value,1000,df)=P-value
pg. 581
How do you find the critical vaule?
use the chart given and it will always be a positive number don’t use -/+ just +
pg. 583 and 605
What language do you use when addressing if Hsub0 is a “good fit”?
reject Hsub0 or fail to reject Hsub0
if the P-value is low, reject H0
The Hsub0 will always be asking if that claim is a “good fit”
pg. 582 and 584
What is the flow chart for wording the final conclusion?
Does the claim say goodfit?-yes-reject Hsub0?-yes-reject
Does the claim say goodfit?-yes-reject Hsub0?-no-not reject
Does the claim say goodfit?-no-reject Hsub0?-yes-support
Does the claim say goodfit?-no-reject Hsub0?-no-not support
same as before just asking if it’s a goodfit instead of equal
pg. 586
What are the steps on the test?
a) find x^2
b) find critical value
c) find P-value
d) reject H0 or fail to reject H0
e) state conclusion
pg. 588
How do you find the expected frequencies when diff categories are expected to have DIFF proportions?
E=np
n is the total number of data values and p is the expected proportion for each category
-n is total observed frequency to find expected frequency take total observed frequency times expected proportion for each section
example on pg 592
pg. 590
