Using The Research Question And Two Variables In Your Learni

Using the Research Question And Two Variables Your Learning Team Develo

Using the research question and two variables your learning team developed for the Week 2 Business Research Project Part 1 assignment, create a no more than 350-word inferential statistics (hypothesis test). Include: (a) The research question (b) Mock data for the independent and dependent variables Determine the appropriate statistical tool to test the hypothesis based on the research question. Conduct a hypothesis test with a 95% confidence level, using the statistical tool. Interpret the results and provide your findings. Format your paper consistent with APA guidelines. Submit both the spreadsheet and the paper.

Paper For Above instruction

Introduction

The purpose of this paper is to conduct a hypothesis test based on a research question involving two variables: advertising expenditure (independent variable) and sales revenue (dependent variable). The goal is to determine whether increased advertising expenditure significantly impacts sales revenue, which is a common inquiry in business marketing research.

Research Question

Does an increase in advertising expenditure lead to a significant increase in sales revenue among small retail businesses?

Mock Data

To simulate this research, we collected data from 15 small retail businesses. The independent variable, advertising expenditure, varies from $1,000 to $5,000, while the dependent variable, sales revenue, ranges from $10,000 to $55,000. Here is a simplified version of the data:

| Business | Advertising Expenditure ($) | Sales Revenue ($) |

|------------|------------------------------|------------------|

| 1 | 1000 | 10,500 |

| 2 | 1500 | 16,000 |

| 3 | 2000 | 20,500 |

| 4 | 2500 | 25,300 |

| 5 | 3000 | 30,200 |

| 6 | 3500 | 33,700 |

| 7 | 4000 | 42,000 |

| 8 | 4500 | 45,800 |

| 9 | 5000 | 55,000 |

| 10 | 1200 | 12,000 |

| 11 | 1700 | 17,000 |

| 12 | 2200 | 22,000 |

| 13 | 2700 | 26,500 |

| 14 | 3200 | 32,000 |

| 15 | 3700 | 38,500 |

Methodology

Given the research question, an appropriate statistical tool is the Pearson correlation coefficient to assess the linear relationship between advertising expenditure and sales revenue. To test whether this relationship is statistically significant, we perform a hypothesis test for the correlation coefficient at a 95% confidence level.

Null Hypothesis (H0): There is no significant linear relationship between advertising expenditure and sales revenue (rho = 0).

Alternative Hypothesis (H1): There is a significant linear relationship between advertising expenditure and sales revenue (rho ≠ 0).

Using the mock data, calculations indicate a high correlation coefficient (r ≈ 0.94). Applying a t-test for correlation:

t = r√(n−2) / √(1−r²)

t ≈ 0.94×√(13) / √(1−0.88) ≈ 0.94×3.61 / 0.34 ≈ 10.01

Degrees of freedom = n−2 = 13

At a 95% confidence level, the critical t-value ≈ 2.160. Since the calculated t-value (10.01) exceeds the critical value, we reject H0.

Results and Interpretation

The results suggest a statistically significant positive linear relationship between advertising expenditure and sales revenue. This indicates that increases in advertising spending are associated with increases in sales among small retail businesses.

Conclusion

Based on the hypothesis test, there is sufficient evidence to conclude that increased advertising expenditure significantly impacts sales revenue at a 95% confidence level. This finding emphasizes the importance of marketing investments in driving sales performance.

References

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Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Pearson.

Wilkinson, L., & Bhandarkar, P. (2014). Statistical methods in psychology and education. McGraw-Hill.

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