Multiple Choice
Which of the following is not a characteristic of the distribution?
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13. Chi-Square Tests & Goodness of Fit
Goodness of Fit Test
Multiple Choice
Which of the following is not a characteristic of the distribution?
A
It is always positively skewed, especially for small degrees of freedom.
B
As the degrees of freedom increase, the distribution becomes more symmetric.
C
It can take on negative values.
D
Its mean is equal to its degrees of freedom.
Verified step by step guidance1
Understand the nature of the chi-square distribution: it is a continuous probability distribution that arises from the sum of the squares of independent standard normal random variables.
Recall that the chi-square distribution is defined only for non-negative values because it is based on squared terms, so it cannot take on negative values.
Review the shape characteristics: the distribution is positively skewed, especially when the degrees of freedom (df) are small, and it becomes more symmetric as df increases.
Remember the mean of the chi-square distribution is equal to its degrees of freedom, i.e., \(\text{mean} = df\).
Identify the statement that contradicts these properties: since the chi-square distribution cannot be negative, the statement 'It can take on negative values' is not a characteristic of the chi-square distribution.
