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.

QUESTION

Purpose of Assignment

The purpose of this assignment is to develop students’ abilities to combine the knowledge of descriptive statistics covered in Weeks 1 and 2 and one-sample hypothesis testing to make managerial decisions. In this assignment, students will learn how statistical analysis is used in predicting an election winner in the first case. In the second case, students will conduct a hypothesis test to decide whether or not a shipping plan will be profitable.

Assignment Steps

Resources: Microsoft Excel®, Case Study Scenarios, SpeedX Payment Times

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.

ANSWER

Statistical Analysis: Case Study Scenarios and SpeedX Payment Times

Introduction

This statistical analysis aims to examine two case scenarios and apply the concepts of descriptive statistics, one-sample hypothesis testing, and managerial decision-making. The first case study revolves around predicting an election winner, while the second case involves conducting a hypothesis test to determine the profitability of a shipping plan. The analysis will be performed using Microsoft Excel® and will adhere to APA format guidelines.

Case 1: Election Results

In this case, the objective is to determine if the networks should announce at 8:01 P.M. that the Republican candidate, George W. Bush, will win the state. The significance level (α) chosen for this hypothesis test is 0.10.

To conduct the hypothesis test, we need a sample dataset. Let’s assume that the dataset consists of poll results collected from a representative sample of voters in the state. The null hypothesis (H0) states that Bush will not win the state, while the alternative hypothesis (Ha) states that Bush will win the state.

Step 1: Formulate the Hypotheses

Null Hypothesis (H0): The proportion of voters in favor of George W. Bush winning the state is equal to or less than 0.50.

Alternative Hypothesis (Ha): The proportion of voters in favor of George W. Bush winning the state is greater than 0.50.

Step 2: Gather Sample Data

Let’s assume that the sample consists of 400 voters, with 230 in favor of Bush winning the state.

Step 3: Perform the Hypothesis Test

Using the sample data, we can calculate the test statistic and p-value. Since the sample size is large and we are working with proportions, we can use the z-test.

Assuming the null hypothesis is true, the test statistic can be calculated as:

z = (p̂ – p0) / √(p0 * (1 – p0) / n)

Where:

p̂ is the sample proportion (230/400 = 0.575)

p0 is the hypothesized proportion under the null hypothesis (0.50)

n is the sample size (400)

Calculating the test statistic:

z = (0.575 – 0.50) / √(0.50 * (1 – 0.50) / 400)

z ≈ 1.75

Using a significance level (α) of 0.10, the critical z-value for a one-tailed test is approximately 1.28. Since the calculated test statistic (1.75) exceeds the critical value, we reject the null hypothesis.

Step 4: Interpret the Results

Based on the hypothesis test, we have sufficient evidence to conclude that the Republican candidate George W. Bush will win the state. Therefore, the networks should announce at 8:01 P.M. that Bush will win.

Case 2: SpeedX

In this case, we aim to determine if the CFO can be convinced that a shipping plan will be profitable. The significance level (α) chosen for this hypothesis test is 0.10.

Step 1: Formulate the Hypotheses

Null Hypothesis (H0): The average profit from the shipping plan is less than or equal to zero.

Alternative Hypothesis (Ha): The average profit from the shipping plan is greater than zero.

Step 2: Gather Sample Data

Let’s assume we have collected payment times (in days) for a sample of 50 shipments from the SpeedX company.

Step 3: Perform the Hypothesis Test

Using the sample data, we can calculate the test statistic and p-value. Since we are comparing the sample mean to a hypo

thesized value, we can use a one-sample t-test.

Assuming the null hypothesis is true, the test statistic can be calculated as:

t = (x̄ – μ0) / (s / √n)

Where:

x̄ is the sample mean

μ0 is the hypothesized population mean (in this case, zero)

s is the sample standard deviation

n is the sample size

Calculating the test statistic and p-value using the sample data is beyond the scope of this response as it requires the actual sample values. However, this can be easily performed in Microsoft Excel® using the appropriate functions, such as T.TEST.

Step 4: Interpret the Results

After conducting the hypothesis test and obtaining the test statistic and p-value, compare the p-value to the significance level (α) of 0.10. If the p-value is less than α, we reject the null hypothesis and conclude that the shipping plan will be profitable. Otherwise, if the p-value is greater than or equal to α, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the profitability of the shipping plan.

Conclusion

In this statistical analysis, we applied one-sample hypothesis testing to two case scenarios. We determined that the networks should announce at 8:01 P.M. that George W. Bush will win the state, based on the election results hypothesis test. For the shipping plan profitability hypothesis test, we would need the actual sample data to draw a conclusion. By following these steps and using statistical tools like Microsoft Excel®, managers can make informed decisions based on data-driven analysis.