In a Chi Square Goodness of Fit Test, how do you calculate the expected value for each category?

• A. Subtract the observed frequency from the total number of observations ($n-O$)
• B. Add the observed frequencies of all other categories
• C. Multiply the total number of observations by the hypothesized proportion for that category ($E=np$)
• D. Divide the observed frequency by the total number of categories ($\frac{O}{k}$)

Answer: (C)

Verified step by step guidance

1. Understand that in a Chi Square Goodness of Fit Test, the expected value for each category represents the frequency we would expect if the null hypothesis is true.
2. Identify the total number of observations, often denoted as \(N\), which is the sum of all observed frequencies across categories.
3. Determine the hypothesized proportion for each category, denoted as \(p_i\), which comes from the null hypothesis or theoretical distribution.
4. Calculate the expected frequency for each category using the formula: \(E_i = N \times p_i\), where \(E_i\) is the expected frequency for category \(i\).
5. Use these expected frequencies to compare against the observed frequencies when computing the Chi Square test statistic.