Prior To Beginning Work On This Discussion Forum Read 367645

Question

Prior To Beginning Work On This Discussion Forum Read Chapter 9 Hypo Prior to beginning work on this discussion forum, read Chapter 9: Hypothesis Testing. Apex Sports is considering entering the golf ball market. The company will make a profit if its market share exceeds 15%. A survey indicates that 128 out of 758 golf ball purchasers would buy an Apex Sports golf ball. In your initial post, answer the following questions: Is the market survey alone sufficient evidence to persuade Apex Sports to enter the golf ball market? How would you use hypothesis testing to help make this decision if you required 90% confidence? Does hypothesis testing support or not support entering the market? Show all your work. Besides the survey results, what other factors might influence the decision? If Apex Sports decides to enter, what are their probabilities of success?

Dr. Jack HW Helper · Accepted Answer

Introduction The decision for Apex Sports to enter the golf ball market hinges on an analysis of market research data and statistical inference. While a survey indicating that 128 out of 758 potential customers would purchase Apex's golf balls provides initial insight, making an informed decision requires rigorous hypothesis testing to evaluate whether the observed proportion exceeds the critical threshold of 15%. This paper discusses whether the survey data suffice as evidence, how to employ hypothesis testing with 90% confidence, and other considerations influencing the market entry decision. Ultimately, it also estimates the probabilities of success based on statistical analysis. Assessing the Sufficiency of the Market Survey Data The market survey shows that approximately 16.91% of potential consumers (128/758) would buy Apex’s golf ball, which appears to surpass the critical 15% threshold necessary for profitability. However, this raw percentage alone is insufficient for a final decision because survey data are subject to sampling variability. To determine whether this observed proportion provides convincing evidence that the true market share exceeds 15%, a formal hypothesis test must be conducted. Hypothesis Testing Process The null hypothesis (H₀) assumes that the true proportion of buyers in the population is equal to 15% (p = 0.15), while the alternative hypothesis (H₁) posits that the true proportion exceeds 15% (p > 0.15). Formally: - H₀: p = 0.15 - H₁: p > 0.15 Given the sample size (n = 758) and the number of favorable responses (x = 128), the sample proportion ($\hat{p}$) is calculated as: $$ \hat{p} = \frac{128}{758} \approx 0.1689 $$ The test statistic for a one-proportion z-test is: $$ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}} $$ Substituting the values: $$ z = \frac{0.1689 - 0.15}{\sqrt{\frac{0.15 \times 0.85}{758}}} \approx \frac{0.0189}{0.0126} \approx 1.50 $$ At a 90% confidence level (significance level $\alpha = 0.10$

Prior To Beginning Work On This Discussion Forum Read 367645

Prior To Beginning Work On This Discussion Forum Read Chapter 9 Hypo

Paper For Above instruction

Introduction

Assessing the Sufficiency of the Market Survey Data

Hypothesis Testing Process

Additional Considerations

Probabilities of Success

Conclusion

References