Question

Which of the following is a characteristic of the chi-square distribution? Select all correct answers.

Select all that apply:

• The total area under the χ2-curve is equal to the degrees of freedom, df.

• The mean of the chi-square distribution is located to the left of the peak.

• The chi-square curve is skewed to the right.

• The chi-square curve is skewed to the left.

Answer 1

Question

Solution :-

Selecting all the correct answer-

4. The chi-square curve is skewed to the right.

Explanation:-

If we look at the chi-square distribution in picture it looks like this-

We can see in this picture that chi-square distribution is right skewed. Only if the the digree of freedom of chi-square distribution is very high then we can say that it is approaches normal distribution,

Explanation for all incorrect answers-

1. The area under chi-square distribution is equal to the degree of freedom.

This is incorrect because area of chi-square distribution like any other valid distribution must be equal to 1.

On the top of that we know that it the mean value of chi-square distribution that is equal to degree of freedom.

2. Mean of the chi-square distribution is located to the left of the peak.

This is incorrect because as we can see in the figure that chi-square distribution is right skewed distribution. Hence its mean must lie right of the peak. This is generally true to assume that mean of right skewed distribution is to the right of the peak.

4. Chi-square distribution is skewed to the left.

As we can see in the picture that chi-square distribution is skewed to the right. Hence this statement is also incorrect.