Question:
If the observed frequencies exactly match expected frequencies, then what is \(\chi^2\) (Chi-square) value?
If the observed frequencies exactly match expected frequencies, then what is \(\chi^2\) (Chi-square) value?
Show Hint
If
\[
O=E,
\]
then
\[
\boxed{\chi^2=0.}
\]
Updated On: Jul 23, 2026
- \(\chi^2\gt 1\)
- \(\chi^2\lt 1\)
- \(\chi^2=0\)
- \(\chi^2=1\)
Show Solution
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The Correct Option is C
Solution and Explanation
The Chi-square statistic is
\[
\chi^2=\sum\frac{(O-E)^2}{E},
\]
where \(O\) is the observed frequency and \(E\) is the expected frequency.
If the observed frequencies exactly equal the expected frequencies,
\[
O=E.
\]
Hence,
\[
(O-E)^2=0
\]
for every class.
Therefore,
\[
\boxed{\chi^2=0.}
\]
Thus,
\[
\boxed{(C)}
\]
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