Question

1. Calculate the expected frequency for each cell and explain the meaning of expected frequencies (15 pts).

Gun Ownership	Types of Residential Area
	Rural	Town	City	Total
Own Gun				555
No Gun				989
Total	593	585	366	1544

Answer 1

The expected frequency is a probability count that appears in contingency table calculations including the chi-square test. Expected frequencies also used to calculate standardized residuals, where the expected count is subtracted from the observed count in the numerator.

• Observed Frequencies are counts made from experimental data. In other words, you actually observe the data happening and take measurements. For example, you roll a die ten times and then count how many times each number is rolled. The count is made after the experiment.
• Expected Frequencies are counts calculated using probability theory. For example, before you roll a six-sided die, you calculate the probability of any one number being rolled as 1/6.