# Statistical Inference

**Statistical Inference **

Overview

Use a provided data file to resolve statistical questions presented in a scenario. Summarize your findings and recommendations in a 1–2 page report for management.

*Note:* The assessments in this course build upon each other, so you are strongly encouraged to complete them in sequence.

When product improvements are made, there is an assumption that the new product will perform better than the previous product. It is important to understand how to select the appropriate statistical tests to determine with a degree of certainty if an improvement has increased the performance of a product.

By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies and assessment criteria:

- Competency 1: Evaluate the quality and fit of data for use in business analysis.
- Determine the null hypothesis and alternative hypothesis for making a product performance comparison.

- Competency 3: Analyze business decision opportunities using basic inferential statistics.
- Compute the appropriate statistical test to determine acceptance or rejection of a null hypothesis.
- Compute the p-value to indicate acceptance or rejection of a null hypothesis regarding a product performance comparison.

- Competency 5: Apply data analysis to general business management planning and decision making.
- Compile findings into a management report with details for recommended actions.

- Competency 6: Communicate in a manner that is professional and consistent with expectations for members of the business professions.
- Communicate in a manner that is professional and consistent with expectations for members of the business professions.

Competency Map

Resources

Required Resources

The following resource contains the data needed to complete the assessment.

Suggested Resources

The following texts provide instruction in Statistics.

- Bowerman, B., O’Connell, R., & Murphree, E. (2014). Business statistics in practice (7th ed.). New York, NY: McGraw Hill.
- Chapter 10, “Comparing Two Means and Two Proportions,” in Business Statistics in Practice, pages 380–404.
- Chapter 11, “Statistical Inferences for Population Variances,” in Business Statistics in Practice, pages 412–424.
- Chapter 12, “Experimental Design and Analysis of Variance,” in Business Statistics in Practice , pages 426–453.

Additional Resources for Further Exploration

The following text provides instruction for statistical analysis in Microsoft Excel.

- Salkind, N. J. (Ed.). (2013). Excel statistics: A quick guide (2nd ed.). Thousand Oaks, CA: Sage
- The following text provides instruction for SAS one of the most commonly used statistical analysis tools in business.
- Slaughter, S. J., & Delwiche, L. D. (2010). The little SAS book for Enterprise Guide 4.2. Cary, NC: SAS Institute. Available from the

The following resource is a tutorial that walks through a number of statistical scenarios.

Statistics Tutorials

This tutorial explains how to select the best team consisting of ten players (from a randomly generated list of 25) and be able to calculate specific statistical values according to the following criteria:

- Barsness, B. (n.d.). Creating the best fantasy baseball team | Transcript. Retrieved from http://www.sophia.org/creating-the-best-fantasy-baseball-team-tutorial

This tutorial introduces Z-scores and their relevance to variance and distribution in data sets.

- Fitz (Producer). (n.d.). Z-scores [Video] | Retrieved from http://www.sophia.org/tutorials/z-scores–6

This tutorial introduces standard error (s) for both sampling distribution models for proportions and means when we do not know the populations parameters p and σ. Demonstrates how to calculate standard error for a proportion.

- Greene, A. (Producer). (n.d.). Standard error [Video] | Transcript. Retrieved from http://www.sophia.org/standard-error-tutorial

This tutorial explains the usefulness of the different sampling methods.

- Varela, A. (Producer). (n.d.). Contrasting sampling methods [Video] | Transcript. Retrieved from http://www.sophia.org/contrasting-sampling-methods/contrasting-sampling-methods–5-tutorial

Additional Statistics Tutorials

This website offers resources that cover many topics in statistics, including presentations that illustrate how to use software to implement statistical methods.

- com (Producer). (n.d.). Independent samples t-test [Video] | Transcript. Retrieved from http://www.statisticslectures.com/topics/independentsamplest/
- com (Producer). (n.d.). Z-test for proportions, two samples [Video] | Transcript. Retrieved from http://www.statisticslectures.com/topics/ztestproportions/
- com (Producer). (n.d.). Independent and dependent samples [Video] | Transcript. Retrieved from http://www.statisticslectures.com/topics/independentdependentsamples/

- Assessment Instructions

Use the Golf Ball Distance Test file, linked in the Resources under the Required Resources heading, to complete the calculations for the scenario for this assessment.

Practical Application Scenario

Your love of golf has brought you back to the range as the new product manager for UniDun’s “Straight Flight” (SF) line of golf balls. The company’s research and development group has been experimenting with dimple patterns that promote straight flight and have achieved some degree of success. You, however, are worried about the effect that the new pattern might have on driving distance.

The Golf Ball Distance Test file 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 to appropriately address the following:

- Identify the null and alternative hypotheses you should form for this test. State each both as a written explanation and as a math equation.
- Identify the appropriate statistical test to accept or reject the null hypothesis.
- Calculate the p-value.
- Summarize your findings and recommendations about the new golf ball product to the vice president of marketing. Your report should not be a statistical analysis of the testing but a summary of the testing results. Assume that your audience is unfamiliar with statistical analysis.

Additional Requirements

Compile your work and report in a 1–2 page Microsoft Word file:

- Paste in the tables you used to make your calculations.
- Clearly title your tables, including each row and column.
- Highlight the results of your data calculations within each table.