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Which of the following is an appropriate description of the chi-square distribution?
A
A chi-square distribution will only contain positive values and will be skewed right, with the skew becoming less pronounced with increasing degrees of freedom.
B
A chi-square distribution will only contain positive values and will be skewed left, with the skew becoming less pronounced with increasing degrees of freedom.
C
A chi-square distribution will only contain positive values and will be skewed right, with the skew becoming more pronounced with increasing degrees of freedom.
E
A chi-square distribution will contain positive and negative values, and will be skewed right, with the skew becoming less pronounced with increasing degrees of freedom.
A chi-square distribution will contain positive and negative values and will be skewed left, with the skew becoming less pronounced with increasing degrees of freedom.



Answer :

GinnyAnswer
Let's break down the properties of the chi-square distribution to find the correct description:

1. Range of Values: The chi-square distribution deals strictly with squared values of normally-distributed data, making all its values positive. Therefore, options suggesting the inclusion of negative values are incorrect.

2. Skewness: The chi-square distribution is known to be skewed to the right. This skewness arises because as the degrees of freedom (df) increase, the distribution spreads out more and becomes more symmetric, but it never shifts to a left skew.

3. Effect of Increasing Degrees of Freedom:
- With fewer degrees of freedom, the chi-square distribution is highly skewed to the right.
- As the degrees of freedom increase, the distribution starts to resemble a normal distribution (bell curve), thereby reducing the skewness. However, it remains right-skewed rather than switching to left-skewed.

Given these points, the correct answer is:

A: A chi-square distribution will only contain positive values and will be skewed right, with the skew becoming less pronounced with increasing degrees of freedom.

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