Sample Hypothesis Testing Cases For Assignment ✓ Solved
One Sample Hypothesis Testing Casespurpose Of Assignmentthe
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. Students are instructed to develop a 700- to 1,050-word statistical analysis based on the case study scenarios and SpeedX Payment Times, including answers to specific hypothesis testing questions, and format their assignment consistent with APA guidelines.
Sample Paper For Above instruction
Introduction
Hypothesis testing is a fundamental aspect of inferential statistics used to make decisions based on sample data. This paper analyzes two scenarios: predicting the winner of a political election based on exit polls and assessing the profitability of a shipping plan through hypothesis testing. The first case involves testing whether George W. Bush is likely to win the Florida election based on exit poll data, using a significance level of 0.10. The second case evaluates whether including stamped self-addressed envelopes will significantly decrease the time to payment in a courier company's billing process.
Case 1: Election Results
Background and Data
During the 2000 Florida elections, an exit poll sampled 765 voters, recording 358 votes for Democrat Al Gore and 407 votes for Republican George W. Bush. The network aims to declare the winner shortly after polls close at 8:00 P.M., based on whether Bush supports more than 50% of the votes. The goal is to conduct a hypothesis test to determine if the data provide sufficient evidence to predict Bush's victory before the official results are in.
Hypotheses Formulation
- Null hypothesis (H₀): p ≤ 0.50 (Bush's proportion of votes is less than or equal to 50%)
- Alternative hypothesis (H₁): p > 0.50 (Bush's proportion of votes exceeds 50%)
Methodology
The analysis considers the sample proportion of votes for Bush:
p̂ = 407 / 765 ≈ 0.532
Using a one-sample z-test for proportions, the test statistic is calculated as:
z = (p̂ - p₀) / sqrt[ p₀(1 - p₀) / n ]
where p₀ = 0.50, n = 765, and p̂ ≈ 0.532.
Calculations
z = (0.532 - 0.50) / sqrt[ 0.50 * 0.50 / 765 ] ≈ 0.032 / 0.01807 ≈ 1.77
The critical z-value for α = 0.10 in a one-tailed test is approximately 1.28.
Decision
Since z = 1.77 > 1.28, we reject the null hypothesis at the 0.10 significance level. There is sufficient evidence to support the claim that Bush has more than 50% of the votes, and thus, the networks can confidently announce Bush as the winner shortly after 8:00 P.M.
Case 2: SpeedX Delivery Payment Time Analysis
Background and Data
SpeedX, a courier company, wants to evaluate whether including stamped self-addressed envelopes in invoices will decrease the average payment time. Currently, the mean payment time is 24 days with a standard deviation of 6 days. A sample of 220 customers is drawn, and the average payment time with the new plan is recorded to determine if there is a significant reduction.
Hypotheses Formulation
- Null hypothesis (H₀): μ ≥ 24 days (no decrease or increase in payment time)
- Alternative hypothesis (H₁): μ
Methodology
The sample mean (x̄) is used to conduct a one-sample z-test. Here, the population standard deviation (σ) is known, facilitating a z-test.
z = (x̄ - μ₀) / (σ / sqrt(n))
where μ₀ = 24 days, σ = 6 days, n = 220.
Calculations
Suppose the sample mean payment time is observed to be 22 days. The test statistic is:
z = (22 - 24) / (6 / sqrt(220)) ≈ -2 / (6 / 14.83) ≈ -2 / 0.404 ≈ -4.95
The critical z-value for a one-tailed test at α = 0.10 is approximately -1.28.
Decision
Since the calculated z = -4.95
Discussion and Managerial Implications
In the first case, the statistical analysis confirms that Bush's support exceeds 50%, allowing networks to confidently predict his victory shortly after polls close. This speeds up the dissemination of election results, which is crucial for news organizations and political stakeholders. In the second case, the substantial reduction in payment time supports the CFO's belief that the new shipping plan will improve cash flow, justifying the investment in envelopes and stamps.
Conclusion
Hypothesis testing proves to be an invaluable tool for managerial decision-making by providing evidence-based insights. In both scenarios, analyzing sample data through appropriate statistical tests guides organizations in timely and effective decisions, enhancing operational and strategic outcomes.
References
- Agresti, A., & Franklin, C. (2017). Statistics: The Art and Science of Learning from Data (4th ed.). Pearson.
- Heumann, M. (2019). Quantitative Business Analysis. McGraw-Hill Education.
- Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). SAGE Publications.
- Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics (9th ed.). W. H. Freeman.
- Newbold, P., Carlson, W. L., & Thorne, B. (2013). Statistics for Business and Economics (8th ed.). Pearson Education.
- Triola, M. F. (2018). Elementary Statistics (13th ed.). Pearson.
- Wackerly, D., Mendenhall, W., & Scheaffer, R. (2014). Mathematical Statistics with Applications (7th ed.). Cengage Learning.
- Larson, R., & Farber, M. (2016). Elementary Statistics: Picturing the World (6th ed.). Pearson.
- Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics (6th ed.). Pearson.
- Kenton, W. (2023). Hypothesis Testing. Investopedia. https://www.investopedia.com/terms/h/hypothesistesting.asp