Questions: Two characteristics of the Chi-square distribution is that: a) Not symmetrical and always skewed to the right b) Symmetrical and always skewed to the right c) Symmetrical and always skewed to the left d) Not symmetrical and always skewed to the left e) None of the preceding

Two characteristics of the Chi-square distribution is that: a) Not symmetrical and always skewed to the right b) Symmetrical and always skewed to the right c) Symmetrical and always skewed to the left d) Not symmetrical and always skewed to the left e) None of the preceding
Transcript text: Two characteristics of the Chi-square distribution is that: a) Not symmetrical and always skewed to the right b) Symmetrical and always skewed to the right c) Symmetrical and always skewed to the left d) Not symmetrical and always skewed to the left e) None of the preceding
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Solution

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Solution Steps

The Chi-square distribution is known to be not symmetrical and always skewed to the right. Therefore, the correct answer is option a).

Step 1: Understanding the Chi-square Distribution

The Chi-square distribution is a continuous probability distribution that is commonly used in statistical inference. It is characterized by its degrees of freedom and is primarily used in hypothesis testing and constructing confidence intervals.

Step 2: Characteristics of the Chi-square Distribution

One of the key characteristics of the Chi-square distribution is that it is not symmetrical. It is always skewed to the right, meaning that the tail on the right side is longer or fatter than the left side. This skewness is a result of the distribution being defined only for non-negative values.

Step 3: Identifying the Correct Option

Given the options provided:

  • a) Not symmetrical and always skewed to the right
  • b) Symmetrical and always skewed to the right
  • c) Symmetrical and always skewed to the left
  • d) Not symmetrical and always skewed to the left
  • e) None of the preceding

The correct characteristic of the Chi-square distribution is option a).

Final Answer

The answer is \( \boxed{A} \).

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