The degrees of freedom (df) for the test statistic is 3.
The conclusion would be Zip code and diet are dependent on one another.
To determine the degrees of freedom (df) for a chi-square test of independence, we use the formula:
df=(r−1)×(c−1)
where
r is the number of rows and
c is the number of columns in the contingency table.
If the researcher has a 4 by 2 contingency table, then
r=4 and c=2. Thus,df=(4−1)×(2−1)=3
So, the degrees of freedom (df) for the test statistic is 3.
To find the p-value associated with the test statistic (13.94), the researcher would refer to a chi-square distribution table or use statistical software. Since the p-value is not provided in the question, I can't give you the exact value. However, I can guide you through the interpretation.
Given the significance level (α) of 0.1, if the p-value is less than 0.1, the researcher would reject the null hypothesis. If the p-value is greater than or equal to 0.1, the researcher would fail to reject the null hypothesis.
If Zip code and diet are found to be independent (i.e., the p-value is greater than 0.1), the conclusion would be:
Zip code and diet are independent of one another.
Zip code and diet are independent of one another.
If Zip code and diet are found to be dependent (i.e., the p-value is less than 0.1), the conclusion would be:
Zip code and diet are dependent on one another.