Instructions:
Data Review:
Begin by reviewing the data you have collected and presented in your contingency table. Ensure that the data is correctly organized and that the totals for each row and column are accurate.
State the Hypotheses:
Null Hypothesis (H₀): State that there is no association between the variables. (e.g., “There is no significant association between gender and preference for sports.”)
Alternative Hypothesis (H₁): State that there is an association between the variables. (e.g., “There is a significant association between gender and preference for sports.”)
Calculate Expected Frequencies:
For each cell in your contingency table, calculate the expected frequency using the formula:
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Record these expected frequencies in a new table.
Compute the Chi-Square Statistic:
Use the formula:
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Where X is the observed frequency, and E is the expected frequency for each cell in your table.
Sum the results for all cells to find the chi-square statistic.
Determine Degrees of Freedom:
Calculate the degrees of freedom for your test:
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Significance Level and Critical Value:
Choose a significance level (commonly Unknown node type: brUnknown node type: brα=0.05).
Using a chi-square distribution table, find the critical value corresponding to your degrees of freedom and significance level.
Decision Rule:
Compare your calculated chi-square statistic to the critical value from the chi-square distribution table.
If your chi-square statistic is greater than the critical value, reject the null hypothesis, indicating that there is a significant association between the variables.
If your chi-square statistic is less than or equal to the critical value, fail to reject the null hypothesis, indicating that there is no significant association between the variables.
Write a Conclusion:
Based on your results, write a conclusion that answers your original research question. Discuss the implications of your findings and any potential limitations of your analysis.
Submission Requirements:
A report containing all the steps outlined above, including your hypotheses, calculations, decision rule, and conclusion.
Attach the original contingency table along with the table of expected frequencies.
Evaluation Criteria:
Accuracy of calculations.
Clarity and logic in the explanation of steps and results.
Completeness of the report, including all necessary statistical components and a thoughtful conclusion.
