Multiple Choice
Which of the following is an appropriate description of the distribution?
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13. Chi-Square Tests & Goodness of Fit
Goodness of Fit Test
Multiple Choice
Which of the following best describes the possible values for a chi-square statistic in a goodness of fit test?
A
The chi-square statistic can take any value greater than or equal to .
B
The chi-square statistic can take any real value, both positive and negative.
C
The chi-square statistic can only take values between and .
D
The chi-square statistic can only take integer values.
Verified step by step guidance1
Recall that the chi-square statistic in a goodness of fit test is calculated using the formula:
\[\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}\]
where \(O_i\) are observed frequencies and \(E_i\) are expected frequencies.
Note that each term in the sum, \(\frac{(O_i - E_i)^2}{E_i}\), is a squared difference divided by a positive expected frequency, so it is always greater than or equal to zero.
Since the chi-square statistic is a sum of non-negative terms, the overall value of \(\chi^2\) cannot be negative; it must be zero or positive.
Understand that the chi-square statistic is not restricted to integer values; it can take any non-negative real number depending on the observed and expected frequencies.
Therefore, the possible values for the chi-square statistic are all real numbers greater than or equal to zero.
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