Develop A 700 To 1050 Word Statistical Analysis Based On The

Developa 700 To 1050 Word Statistical Analysis Based On The Case Stu

Develop a 700- to 1,050-word statistical analysis based on the Case Study Scenarios and SpeedX Payment Times. Include answers to the following: Case 1: Election Results · Use 0.10 as the significance level (α). · Conduct a one-sample hypothesis test to determine if the networks should announce at 8:01 P.M. the Republican candidate George W. Bush will win the state. Case 2: SpeedX · Use 0.10 and the significance level (α). · Conduct a one-sample hypothesis test and determine if you can convince the CFO to conclude the plan will be profitable. Format your assignment consistent with APA format.

Paper For Above instruction

Introduction

Statistical hypothesis testing is a critical tool in decision-making processes across various sectors, including political elections and business planning. In this analysis, two case scenarios are examined: the first involves evaluating whether election results justify an early announcement of a presidential candidate’s victory, and the second assesses the profitability of a business plan initiated by SpeedX. Both cases utilize a significance level (α) of 0.10, reflecting an acceptable risk threshold for type I error in these tests. The objective is to determine whether the statistical evidence supports the respective claims at the specified significance level.

Case 1: Election Results

The first scenario involves determining if the network should declare Republican candidate George W. Bush as the winner of a state election at 8:01 P.M. With current polling data and vote count trends, a one-sample hypothesis test can be performed to evaluate whether the observed vote proportions provide sufficient evidence to confirm Bush’s victory.

The null hypothesis (H₀) assumes that Bush has not yet secured enough votes to be declared the winner at this time, or more formally, that the proportion of votes favoring Bush is less than or equal to the threshold needed for victory. Conversely, the alternative hypothesis (H₁) posits that Bush has indeed reached the critical winning proportion, implying the network can safely announce his victory.

Applying a one-proportion z-test, the test statistic is calculated based on the observed proportion of votes for Bush and the hypothesized proportion reflecting the winning threshold. If the resulting p-value is less than 0.10, the null hypothesis is rejected, indicating sufficient evidence to announce Bush’s win at 8:01 P.M. Conversely, a p-value greater than 0.10 suggests insufficient evidence, and the network should wait for more data before making a declaration.

For example, if preliminary data shows Bush has secured 52% of the vote with a sample size of 10,000 votes, the z-test formula is applied to this sample proportion compared to the hypothesized proportion necessary for victory, such as 50%. The resulting p-value determines whether the evidence is statistically significant enough to support an early announcement.

Case 2: SpeedX Profitability Planning

The second scenario assesses the likelihood that SpeedX’s new business plan will be profitable, based on a sample of pilot test results or projected financial data. The null hypothesis (H₀) states that the plan will not be profitable, or that the mean expected profit is less than or equal to zero, while the alternative hypothesis (H₁) claims that the plan is profitable with a mean profit greater than zero.

Using a one-sample t-test, the analysis compares the sample mean profit against the assumed population mean under H₀. The test considers the sample size, mean, and standard deviation of the profit data. If the calculated p-value falls below 0.10, the null hypothesis is rejected, and the CFO can be convinced that the plan has a statistically significant chance of being profitable.

Suppose the sample mean profit is estimated at $15,000 with a standard deviation of $5,000 across 30 test cases. The t-test assesses whether this mean profit significantly exceeds zero beyond the margin of error, providing evidence to support proceeding with the plan. If the p-value is greater than 0.10, the data does not justify a confident assertion of profitability, and further analysis or data collection may be necessary.

Discussion

Both cases exemplify the importance of hypothesis testing in real-world decision-making, where statistical evidence guides critical timing and financial strategy. The choice of a 0.10 significance level indicates a willingness to accept a 10% risk of incorrectly rejecting the null hypothesis, which balances the need for timely decisions against the possibility of false positives.

In the election context, early declaration decisions hinge on the strength of the vote share data and the robustness of the hypothesis test. A significant p-value supports the contention that the candidate has already secured enough votes, justifying an early announcement to audiences and stakeholders.

Similarly, in the business scenario, the hypothesis test provides a quantifiable measure of the likelihood of success, enabling the CFO and management team to make informed financial commitments. The statistical evidence, if convincingly positive, can justify investments in further development or full-scale deployment.

Conclusion

The application of hypothesis testing in these scenarios demonstrates its vital role in strategic decision-making processes. Using a significance level of 0.10, the election results and SpeedX’s profitability prospects are evaluated quantitatively. In each case, the p-values derived from the tests guide whether to proceed with early declarations or investments, emphasizing the importance of accurate data collection and analysis. These examples underscore that statistical evidence, when properly interpreted, enhances decision accuracy and minimizes risk in complex, real-world situations.

References

  • Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Routledge.
  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). Sage Publications.
  • Ghasemi, A., & Zahediasl, S. (2012). Normality tests for statistical analysis: A guide for non-statisticians. International Journal of Endocrinology and Metabolism, 10(2), 486-489.
  • Hinkle, D. E., Wiersma, W., & Jurs, S. G. (2003). Applied Statistics for the Behavioral Sciences (5th ed.). Houghton Mifflin.
  • McDonald, J. H. (2014). Handbook of Biological Statistics (3rd ed.). Sparky House Publishing.
  • Montgomery, D. C., & Runger, G. C. (2014). Applied Statistics and Probability for Engineers (6th ed.). Wiley.
  • Sheskin, D. J. (2011). Handbook of Parametric and Nonparametric Statistical Procedures (5th ed.). Chapman and Hall/CRC.
  • Nolte, K. G. (2019). Applied Business Statistics: Procedures and Principles (3rd ed.). CRC Press.
  • Ott, R. L., & Longnecker, M. (2010). An Introduction to Statistical Methods and Data Analysis (6th ed.). Brooks/Cole.
  • Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data (2nd ed.). MIT Press.

Related Assignments