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

• A. Add the observed frequencies of all other categories
• B. Subtract the observed frequency from the total number of observations
• C. Divide the observed frequency by the total number of categories
• D. Multiply the $n$ (total number of observations) by the hypothesized proportion $p$ for that category: $E=np$

Answer: (D)

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 about the distribution 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 expected distribution under the null hypothesis.
4. Calculate the expected frequency for each category by multiplying the total number of observations by the hypothesized proportion for that category using the formula: \[ E_i = N \times p_i \] where \(E_i\) is the expected frequency for category \(i\).
5. Repeat this calculation for each category to obtain all expected frequencies needed for the Chi Square Goodness of Fit Test.