i. In the goodness-of-fit test, the chi-square distribution is used to determine how well an observed set of observations "fits" an "expected" set of observations. ii. The sum of the expected frequencies and the sum of the observed frequencies must be equal.
iii. If the computed value of chi-square is less than the critical value, reject the null hypothesis at a predetermined level of significance.
A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

In a goodness-of-fit test, the chi-square distribution is indeed used to compare observed frequencies with expected frequencies, making statement (i) correct. The sum of the expected frequencies must equal the sum of the observed frequencies for the test to be valid, which makes statement (ii) correct. However, statement (iii) is incorrect because if the computed chi-square value is less than the critical value, we fail to reject the null hypothesis, not reject it.

I in the Goodness-Of-Fit Test, the Chi-Square Distribution Is Used