The Golf Ball Distance Test Document In The Resources Contai

The Golf Ball Distance Test Document In The Resources Contains Test Re

The Golf Ball Distance Test document in the Resources contains test results that compare the driving distances for the two different kinds of balls: 40 balls of the new SF type, and 40 of the old UniDun type. Your job is to determine if the old UniDun balls can be driven further than the new SF balls. To resolve this question, you need appropriate answers to the following four questions. Remember to use your MBA6018 – Data Analysis for Business Decisions textbook and any additional resources you may have located to help you answer each question:

• Identify the null and alternative hypotheses you should form for this test. State each as an explanation and as a math equation.
• Identify the appropriate statistical test to accept or reject the null hypothesis.
• Calculate the p-value.
• What should you tell the vice president of marketing about the golf balls product? Hint: You will need to use Excel to calculate the statistical parameters, the Mean, Variance, and Standard Deviation and the Analysis Toolpack or StatPlus: mac LE to calculate the statistical test that you have chosen and the p-value.

Paper For Above instruction

The purpose of this statistical analysis is to evaluate whether the old UniDun golf balls can be driven further than the new SF golf balls, based on the test results documented in the provided resources. This involves formulating hypotheses, selecting appropriate tests, calculating necessary statistical measures, and interpreting the results to inform business decisions.

Formulating the Hypotheses

The first step in any hypothesis test is to establish the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis posits no difference or no effect, serving as a default assumption that there is no significant difference in driving distances between the two types of golf balls. Conversely, the alternative hypothesis suggests that there is a significant difference, specifically that the old UniDun balls can be driven further than the new SF balls. The hypotheses can be explained and expressed mathematically as follows:

• Null hypothesis (H₀): The mean driving distance of the old UniDun balls is less than or equal to the mean driving distance of the new SF balls.
• Alternative hypothesis (H₁): The mean driving distance of the old UniDun balls is greater than the mean driving distance of the new SF balls.

Mathematically, these hypotheses are expressed as:

• H₀: μ₁ ≤ μ₂
• H₁: μ₁ > μ₂

Where μ₁ is the population mean driving distance for the old UniDun balls, and μ₂ is that for the new SF balls.

Choosing the Appropriate Statistical Test

Given that we are comparing the means of two independent samples (each with 40 observations), the suitable statistical test is the independent samples t-test. This test assesses whether there is a statistically significant difference between the means of two independent groups. Since the research question hypothesizes that the old UniDun balls may be driven further, a one-tailed t-test is appropriate to determine if μ₁ > μ₂.

Calculating the p-value

To perform the t-test, the following statistical parameters need to be calculated from the sample data:

• Sample means (x̄₁ and x̄₂)
• Sample variances (s₁² and s₂²)
• Sample sizes (n₁ and n₂ = 40 for each group)

Using Excel's Data Analysis Toolpak or StatPlus, we input the sample data to compute the t-statistic and corresponding p-value. The p-value indicates the probability of observing a t-statistic as extreme as, or more extreme than, the calculated value under the null hypothesis. If the p-value is below the significance level (commonly 0.05), we reject the null hypothesis, suggesting that the old UniDun balls can indeed be driven farther.

Interpreting Results and Business Implication

Suppose the calculations yield a p-value of 0.03, which is less than 0.05. In this case, we reject the null hypothesis and conclude there is statistically significant evidence that the old UniDun balls can be driven further than the new SF balls. Conversely, if the p-value exceeds 0.05, we fail to reject the null hypothesis, implying insufficient evidence to claim a significant difference in driving distances.

Based on these findings, the vice president of marketing should be advised about whether the old UniDun golf balls outperform the new SF balls in terms of driving distance. If the results are significant, marketing strategies can emphasize this competitive advantage. Otherwise, other quality aspects or features should be considered for promotion.

Conclusion

This analysis demonstrates a structured approach to evaluating product performance through statistical testing. The choice of hypotheses, test selection, statistical calculations, and interpretation of the p-value are essential steps that inform data-driven business decisions, ensuring that marketing strategies align with actual product capabilities.

References

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