Question

M6A2 Discussion Forum: Chi-Square Distribution Discussion Board Topic: Discuss the Chi-Square distribution. Discussion Board Guidelines: You will need to respond to a peer's posting, and evidence of critical thinking is required.

Answer 1

Ans ) The square of a standard normal variate is known as a chi-square variate with 1 degree
of freedom (d.f.)

chi - square distribution is denoted by $\chi$ ² .

Conditions for tbe Validity of chi-square test :

1. Chi-square test is an approximate test for large values of n. For the validity of chi-square test of
'goodness oj fit" between theory and experiment, the following conditions must
be satisfIed :

(l) The sample observations should be independent .

(II) Sum of observed frequencies should be equal to sum of expected frequencies .

(III) N, the total frequency should be reasonably large, say, greater than 50.

2 . Applications or Chi-square Distribution :

I) To test if the hypothetical value of the population variance is $\sigma$ ²=$\sigma$²₀ .

II) To test the 'goodness of fit'.

III) To test the independence of attributes.

IV) To test the homogeneity of independent estimates of the population variance.

V) To combine various probabilities obtained from independent experiments to give a single test of significance.

VI) To test the homogeneity of independent estimates of the population correlation coefficient .

Now , formula for chi square goodness of fit is :

$\chi$² =$\sum$ {( oi - ei )² / ei }

where oi is the observed and ei is the expected frequency .

I HOPE I WAS HELPFUL AND HAVE CLEARED YOUR DOUBTS.

THANKYOU .