In general, how do the hypotheses for chi-square tests of independence differ from those for chi-square tests of homogeneity

chi-square test independence is evaluate whether one variable is related to other variable or not. it checks for independency.

chi-square test for homogeneity -  it is used to identify the homogeneity of one variable across the given population.

Step-by-step explanation:

chi-square test - although this test is also dealt with classified data, there is a difference between the chi-square test on independence and the chi-square test of homogeneity

chi-square test independence is evaluate whether one variable is related to other variable or not. it checks for independency.

chi-square test for homogeneity -  it is used to identify the homogeneity of one variable across the given population.

the balance is found at the link

step-by-step explanation:

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.