PART 1 – DATA ANALYSIS (50 points)

Download the provided Excel data file and complete the following analysis:

1. Conduct data exploration to describe the data and identify any potential problems or limitations of the dataset. This should include, but is not limited to, aspects such as descriptive statistics, features of the response variable, and identifying missing data or outliers. This should also include graphical exploration of the data (i.e., histograms, box plots, scatter plots, etc.). Finally, evaluate whether the response variable is normally distributed.

2. Conduct the following series of hypothesis tests to further explore the data taking into account any assumptions or limitations of the tests.

a. The planned production rate is 800 units per hour. Does this sample suggest that we are meeting that threshold?

b. Is there a difference between the average production rates at each facility?

c. Do the two facilities have the same variability in their production rates?

3. Construct a series of One-Way ANOVA models to investigate the effect of each factor on the production rate (total of three models). Conduct post-hoc and residual analysis as appropriate and discuss your conclusions, insights, and recommendations. If appropriate, consider alternative models (e.g., transformations, alternative ANOVAs (e.g., welch), etc.) and discuss the fit or adequacy of the models.

Submit a Technical Report that describes the problem and analysis approach (assumptions, limitations, etc.), summarizes the results of your analysis including screen shots from the Minitab output, discusses findings, and makes recommendations based on the analysis. Also, submit the final Minitab output file. There is no minimum page or formatting requirements but the report must be formal/professional and cannot exceed 10 pages.

PART 2 – SHORT ANSWER (20 points)

Address the following writing prompts as an appendix to the Technical Report.

1. Concisely describe the correct way to interpret a confidence interval and discuss how this differs from common misconceptions (150-500 words).

2. Concisely describe the concepts of Type I Error, Type II Error, and Statistical Power and discuss why these values are needed to assess the rigor of a statistical test (150-500 words).

3. Concisely describe the concept of partitioning variance and the role that Analysis of Variance plays in industrial experimentation (150-500 words).