QQuestionStatistics
QuestionStatistics
"Which of the following best describes the shape of the chi-square distribution when the degrees of freedom are less than 10?
A. Unimodal and symmetric
B. Skewed to the right
C. Skewed to the left
D. Uniform
E. Bimodal"
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understanding the Chi-Square Distribution
The chi-square distribution is a probability distribution that is always right-skewed (positively skewed), especially when the degrees of freedom are small.
Step 3:: Characteristics of Chi-Square Distribution with Low Degrees of Freedom
- When degrees of freedom are less than 10, the distribution has a distinct shape - It is not symmetric - It has a longer tail on the right side - The peak is not centered but shifted to the left
Step 4:: Visual Interpretation
- As degrees of freedom increase, the distribution becomes more symmetric - With fewer degrees of freedom (< 10), the skewness is more pronounced - The distribution starts with a peak near zero and has a long right tail
Step 5:: Identifying the Correct Answer
Based on the characteristics described, the distribution is skewed to the right.
Final Answer
Skewed to the right Explanation: The chi-square distribution with degrees of freedom less than 10 is characterized by a right-skewed (positively skewed) shape, with the peak of the distribution shifted to the left and a long tail extending to the right.
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