Question Set C Prompt:

Which of the following of statements is true of chi-square distribution? Mark all that are true.

Question

Question Set C Prompt:

Which of the following of statements is true of chi-square distribution? Mark all that are true.

BlackTom AI · Accepted Answer

Question restatement: The prompt asks which statements about the chi-square distribution are true, and to mark all that apply.
Option 1: 'They take on only positive values.' This is correct because a chi-square distribution is defined as a sum of squared standard normal variables, which cannot be negative, so the support is x > 0. The distribution thus has a nonnegative domain and is strictly positive for x > 0, with density concentrated on the positive real line.
Option 2: 'As the number of degrees of freedom increases, their density curves look more and more like a normal distribution.' This is also correct. The chi-square with k degrees of freedom can be viewed as a gamma distribution with shape k/2 and scale 2. As k grows large, by the central limit type effect and the gamma-to-normal approximation, the distribution becomes more symmetrical and its standardized form approaches a normal curve, with mean k and variance 2k. This explains the increasing resemblance to normal curves for larger df.
Why the other possibilities are not present here: There are no additional options to evaluate, but note that a common misperception is that the chi-square distribution could take negative values or that its shape never resembles a normal; both are incorrect because of its nonnegative support and its large-sample normal approximation behavior, respectively. The two provided statements are consistent with the defining properties and asymptotic behavior of the chi-square distribution.

Su25-STATS-141-01/BIO-141-01 Homework 4: Chi-Square Goodness-of-Fit Test, Causation Claims, & Generalization Claims

Question Set C Prompt: Which of the following of statements is true of chi-square distribution? Mark all that are true.

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