Perform A Chi Square Test On The Data Below Present Your Fin

Perform A Chi Square Test On The Data Below Present Your Findings

Perform a Chi-square test on the data below. Present your findings. What can you conclude from your results? Explain.

Write a one to two (1–2) page short paper in which you perform a Chi-square test on data, present your findings and conclusion. The data involves the categories Hot Dogs and Hamburgers with observed counts for Men and Women.

Paper For Above instruction

The application of the Chi-square test is a fundamental statistical technique used to determine whether there is a significant association between categorical variables. In this case, the data pertains to preferences for hot dogs and hamburgers among men and women. The key objective is to analyze whether gender has an influence on the choice of food, reflecting differences in preferences across these groups.

The data provides counts of men and women who prefer hot dogs or hamburgers. To perform the Chi-square test, expected frequencies are calculated under the null hypothesis that gender and food preference are independent. The observed counts are compared to these expected counts, and the Chi-square statistic is computed to assess the deviation. If the calculated Chi-square exceeds the critical value at a defined significance level (commonly 0.05), we reject the null hypothesis, indicating a statistically significant relationship between gender and food preference.

Suppose, for example, that the observed counts are as follows: 40 men prefer hot dogs, 10 men prefer hamburgers, 30 women prefer hot dogs, and 30 women prefer hamburgers. The total counts are used to determine expected frequencies based on the marginal totals, assuming independence. The expected count for men preferring hot dogs, for example, would be calculated as the total number of men multiplied by the total number of hot dog preferences, divided by the overall total. Similar calculations are performed for each cell in the contingency table.

After calculating the expected counts, the Chi-square statistic is obtained by summing the squared differences between observed and expected counts divided by the expected counts across all cells. This value is then compared to the Chi-square distribution table value with the appropriate degrees of freedom (df), which in this case is (rows-1) * (columns-1) = 1.

If the test indicates significance, we conclude that there is an association between gender and food preference. For instance, if men are found to prefer hot dogs significantly more than women, this might reflect underlying cultural or social factors. Conversely, if the result is not significant, we assume there is no strong evidence to suggest a relationship, and preference may be independent of gender. This analysis provides insights into consumer behavior, which could inform marketing strategies or further sociological research.

References

• Agresti, A. (2007). An Introduction to Categorical Data Analysis. John Wiley & Sons.
• Everitt, B. (2002). The Cambridge Dictionary of Statistics. Cambridge University Press.
• McHugh, M. L. (2013). The Chi-square test of independence. Biochemia Medica, 23(2), 143-149.
• Conover, W. J. (1999). Practical Nonparametric Statistics. John Wiley & Sons.
• Shimberg, B., &li, M. (2010). Principles of Statistical Inference. Chapman & Hall.