For the chi-square tests in the analysis of categorical data, the rejection region 1.is always located in the lower tail of the distribution. 2.is alw

allhvasstH 2021-02-20 Answered
For the chi-square tests in the analysis of categorical data, the rejection region
1.is always located in the lower tail of the distribution.
2.is always equally split in the two tails of the distribution.
3.is always located in the upper tail of the distribution.
4.depends on the probability of a type II error.
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Expert Answer

unett
Answered 2021-02-21 Author has 119 answers
Step 1
Chi-Square test for independence:
In the test for independence, we test whether there is an association between the categorical variables.
Null hypothesis: There is no association between the two categorical variables.
Alternative hypothesis: There is an association between the two categorical variables.
Step 2
Here, to test the association between categorical variables, the critical region is always located in the upper tail of the distribution.
That is, Option 3 is correct.
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New questions

Linear multivariate recurrences with constant coefficients
In the theory of univariate linear recurrences with constant coefficients, there is a general method of solving initial value problems based on characteristic polynomials. I would like to ask, if any similar method is known for multivariate linear recurrences with constant coefficients. E.g., if there is a general method for solving recurrences like this:
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Moreover, is their any method for solving recurrences in several variables, when the recurrence goes only by one of the variables? E.g., recurrences like this:
f ( n + 1 , m ) = f ( n , 2 m ) + f ( n 1 , 0 ) , f ( 0 , m ) = m .
This second question is equivalent to the question, if there is a method of solving infinite systems of linear univariate recurrences with constant coefficients. That is, using these optics, the second recurrence becomes f m ( n + 1 ) = f 2 m ( n ) + f 0 ( n 1 ) , f m ( 0 ) = m , m = 0 , 1 , .
I am not interested in a solution of any specific recurrence, but in solving such recurrences in general, or at least in finding out some of the properties of possible solutions. For instance, for univariate linear recurrences, each solution has a form c 1 p 1 ( n ) z 1 n + + c k p k ( n ) z k n ,, where c i 's are constants, p i 's are polynomials and z i 's are complex numbers. Does any similar property hold for some class of recurrences similar to what I have written?
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