2.10.2 Hypothesis Testing

Using the chi-squared test on its own isn't enough to formally declare independence. There is a procedure to determine if the two classifications are independent or not.

Step 1: State the null hypothesis. The null hypothesis is a statement that the two classifications are being considered are independent. The null hypothesis takes the notation H₀. We also state an alternative hypothesis. Either the null hypothesis or the alternative hypothesis must be true, so H₁ indicates that the two classifications are not independent. The alternative hypothesis takes the notation H₁.

Step 2: Calculate the degrees of freedom according to

Step 3: State the significance level required, i.e. 10%, 5%, 1%

Step 4: We state the rejection (of H₀) inequality where k is determined from the table of critical values. This table is found on page 594 and is likely given in your formula package.

Step 5: Find using the formula from last class.

Step 6: We either accept H₀ or H₁, depending on the rejection equality result.

Step 7: If operating at the 5% level, we couuld also use the p-values to help us with our decision making. If p>0.05, accept H₀, if p<0.05, accept H₁.

After arriving at a conclusion, state it if appropriate (paper 1 or paper 2)

Ex 1 p.596#2a

p. 596#1-6 (we just did 2a)