When conducting a chi-square goodness-of-fit test, how are the expected counts for each category calculated?

• A. By dividing the observed count in each category by the total number of categories ($\frac{O}{k}$)
• B. By subtracting the observed count from the total sample size for each category ($N-O$)
• C. By taking the square root of the observed count in each category ($\sqrt{O}$)
• D. By multiplying the total sample size by the hypothesized proportion for each category ($E=Np$)

Answer: (D)

Verified step by step guidance

1. Understand that in a chi-square goodness-of-fit test, we compare observed counts to expected counts to see if the observed data fits a hypothesized distribution.
2. Identify the total sample size, denoted as \(N\), which is the sum of all observed counts across categories.
3. Determine the hypothesized proportion for each category, denoted as \(p_i\), which represents the expected fraction of the total sample in that category under the null hypothesis.
4. Calculate the expected count for each category by multiplying the total sample size by the hypothesized proportion: \(E_i = N \times p_i\).
5. Use these expected counts \(E_i\) along with the observed counts \(O_i\) to compute the chi-square test statistic.