In a chi-square goodness-of-fit test, what are the observed counts and expected counts?

In a chi-square goodness-of-fit test, what are the observed counts and expected counts?

• A. Observed counts come from data; expected counts are the counts expected under the hypothesized distribution
• B. Observed counts come from theoretical distribution; expected counts come from data
• C. Observed counts are the same as expected counts
• D. Observed counts come from the hypothesized distribution; expected counts come from data

Answer: (A)

In a chi-square goodness-of-fit test, you’re comparing what you actually saw in the data to what the theory says you should see if the data followed the proposed distribution. The observed counts are the real counts in each category from your sample. The expected counts are what you would expect in each category under the hypothesized distribution, calculated as the total sample size times the probability of each category under that distribution. This setup lets you judge whether any differences are just due to random variation or indicate a mismatch with the model. So the observed counts come from data, and the expected counts come from the hypothesized distribution.

In a chi-square goodness-of-fit test, you’re comparing what you actually saw in the data to what the theory says you should see if the data followed the proposed distribution. The observed counts are the real counts in each category from your sample. The expected counts are what you would expect in each category under the hypothesized distribution, calculated as the total sample size times the probability of each category under that distribution. This setup lets you judge whether any differences are just due to random variation or indicate a mismatch with the model. So the observed counts come from data, and the expected counts come from the hypothesized distribution.