From A Survey Of 1000 Families: Two-Way Table

From A Survey Of 1000 Families The Following Two Way Table Was Cons

From a survey of 1,000 families, the following two way table was constructed: Owned Product X | Income level | Yes | No | High | Medium | Low

Is there a statistically significant relationship between income level and ownership of product X at the 95 percent confidence level?

Paper For Above instruction

The investigation of the relationship between income level and ownership of product X among a surveyed population of 1,000 families presents an intriguing statistical inquiry. This analysis aims to determine whether income level significantly influences the likelihood of owning product X, based on the collected data. The two-way table, which categorizes families by their income levels—high, medium, and low—and their ownership status—yes or no—serves as the foundational data set for this analysis.

Introduction

Understanding consumer behavior and purchasing decisions often involves examining the relationship between demographic factors such as income levels and product ownership. The hypothesis addressed here is whether income level impacts the likelihood of owning product X. Establishing this relationship not only supports targeted marketing strategies but also enhances comprehension of the socioeconomic factors that influence purchasing patterns.

Methodology

The statistical approach employed involves the Chi-square test of independence, a non-parametric test suitable for examining relationships between categorical variables. The data from the survey was organized into a contingency table, summarizing the counts of families in each category:

  • High income families owning or not owning product X
  • Medium income families owning or not owning
  • Low income families owning or not owning

Assuming the table data was collected accurately, the Chi-square test calculates the expected frequencies under the null hypothesis that income level and ownership status are independent. The observed frequencies are then compared to these expected values to determine if the variations are statistically significant.

Results

The analysis involves computing the Chi-square statistic and associated p-value. If the p-value is less than the significance level of 0.05 (corresponding to a 95% confidence level), the null hypothesis of independence is rejected, indicating a statistically significant relationship between income level and ownership of product X.

For example, suppose the computed Chi-square value exceeds the critical value from the Chi-square distribution table or the p-value is less than 0.05. In that case, we conclude that income level and ownership are associated. If not, the data does not provide sufficient evidence to support a relationship.

Discussion

If the statistical analysis indicates a significant relationship, it suggests that income level influences the decision to own product X. Higher income families might be more likely to own the product, possibly due to affordability or perceived value, whereas lower income families may not. Conversely, if no significant relationship is found, factors other than income might play a more crucial role, such as marketing efforts, product availability, or cultural preferences.

The implications of these findings are relevant for marketers and policymakers aiming to promote equitable access to products like X across different socioeconomic strata. Moreover, understanding these dynamics helps in designing more effective marketing campaigns tailored to specific income groups.

Limitations and Further Research

The analysis is limited by the data provided; raw counts and detailed percentages would enhance the robustness of conclusions. Additionally, factors such as geographic location, education, and cultural influences were not considered but might impact ownership decisions. Future research could incorporate multivariate analysis to account for these variables and provide a more comprehensive understanding of consumer behavior.

Conclusion

Based on the Chi-square test of independence, if the p-value obtained was less than 0.05, we conclude that there is a statistically significant relationship between income level and ownership of product X at the 95 percent confidence level. This indicates that income influences the likelihood of owning product X among surveyed families, which has important implications for targeted marketing strategies and socioeconomic policy development.

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