Final answer:
To study the relationship between religious affiliation and geographical region in City K, a chi-square test of independence would be most appropriate. This statistical test compares categorical data from random samples in both regions. Results help determine if a significant relationship exists, avoiding ecological fallacies by using representative and methodologically sound approaches.
Step-by-step explanation:
To study the relationship between religious affiliation and geographical region in City K, the appropriate statistical method would be to conduct a chi-square test of independence. This test is used to determine whether there is a significant association between two categorical variables. Since religious affiliation and geographical region are both categorical variables, this test is suitable.
To begin, you would collect data on religious affiliations from both the Northern and Southern parts of City K, ensuring you have a random sample from each. Once the data are collected, you would organize it into a contingency table reflecting the frequencies of each religious affiliation within both Northern and Southern samples. Using the contingency table, you would then calculate the chi-square statistic and evaluate it against a critical value from the chi-square distribution to determine if differences in religious affiliation are likely due to chance, or if they're statistically significant. It is important to consider the size of the samples and to ensure they are representative of the populations in both regions. The ecological fallacy must be avoided, which occurs when assumptions are made about individuals based on group-level data. By using a random sampling method and appropriate statistical analysis, your study is more likely to produce valid conclusions about the relationship between religious affiliation and geographical region in City K.