Questions: Which of the following best describes the possible values for a chi-square statistic? Chi-square is always a positive whole numbers. Chi-square is always positive but can contain fractions or decimal values. Chi-square can be either positive or negative but always is a whole number. Chi-square can be either positive or negative and can contain fractions or decimals.

Solution Steps

The chi-square statistic is a measure used in statistics to assess how expectations compare to actual observed data. It is commonly used in hypothesis testing, particularly in tests of independence and goodness-of-fit tests.

The chi-square statistic is always non-negative. This is because it is calculated as the sum of squared differences between observed and expected frequencies, divided by the expected frequencies. Since squaring any real number results in a non-negative value, the chi-square statistic cannot be negative. Additionally, the chi-square statistic can take on fractional or decimal values, as it is not restricted to whole numbers.

Given the properties of the chi-square statistic, we can evaluate the options:

• Option A: "Chi-square is always a positive whole number." This is incorrect because the chi-square statistic can be a decimal or fractional value.
• Option B: "Chi-square is always positive but can contain fractions or decimal values." This is correct because the chi-square statistic is always non-negative and can be a decimal or fractional value.
• Option C: "Chi-square can be either positive or negative but always is a whole number." This is incorrect because the chi-square statistic cannot be negative and is not restricted to whole numbers.
• Option D: "Chi-square can be either positive or negative and can contain fractions or decimals." This is incorrect because the chi-square statistic cannot be negative.

Final Answer