case study

 

Complete Session 4 Case Study: Case Study 10.1 in the textbook.

Submit a Word document formatted in APA style complete with cover and reference pages.  The reference page must have at least one entry:  the textbook.  

The submission must be a form Research Report with the following parts:

Background information about the case:  The section must provide information about the people, places, operations, business, etc. and the research question or practical business challenges for which the current research will be used to provide a solution .  This section need not be long; up to two well written paragraphs are usually sufficient. 

Descriptive Statistics and Data illustration:  In this section, the submission must summarize how the data was obtained (see chapter 1 of the text). Graphs and charts illustrating the main features of the data are also required – please see chapter 2 of the textbook.   Finally, a table of descriptive statistics accompanied by  description and explanations of the main features of the data are also required.

Statistical Method:  This part of the submission must explain the main statistical method(s) used in the case.   What is the theory behind it? What are the working hypotheses (null and alternative, etc.), what main measures, statistics, or parameters etc.,  are to be estimated or calculated using the method; how does it measures or calculates these measures, statistics, or parameters?  Finally, this section must describe how the results of the statistical method are interpreted. That is, what is it about the results that would indicate that the working hypotheses or research questions are confirmed or rejected or perhaps need to be modified and tested again? 

Results:  The actual results of the statistical method applied to the data are now presented in this section.  The section requires the student to describe the results and their theoretical interpretation based on the description of the method described in the previous section.

Conclusion and Recommendation:  This section restates the statistical results and applies it to the business situation in the case.  It also makes practical recommendations about what steps the business in the case can take going forward based on the results of the statistical analysis.  The application and recommendation can take one or more of these general forms.

The statistical results of the data analysis provided an answer(s) to the issues that the business is facing.  As a result specific policies or practical steps can be implemented in the business. 
 The statistical results of the data analysis provided only partial answers.  More research and tests need to be done to come up with a more useful answers for the business situation.
The statistical results did not provide any useful information for the challenges that a business(s) is facing.  Recommendations for conducting new research with new approaches, data, variables, etc. may be required. 

Note

:  there is always room for ‘further research’ since it is impossible for a single research case to answer every possible question. 

Note

1. The textbook provides narratives, questions, or actual steps/questions for each case study.  While these are useful for conducting actual research, the submission must take the form of a research report and follow the above pattern.
2. Excel has routines for comparing two population sample means under the Data Analysis tool kit.  Follow the Excel guides in the textbook to apply this technique to the current problem.
3. Consistent with the emphasis of this course on interpretation, an edited version of the answer key for the case study have been provided here.  Students are required to use the information to enhance their understanding of the statistical methods and the results obtained.  

Case 1

0

.1: Motive Power Company-Part 1

The key issue is to determine if statistical evidence is sufficient to conclude a difference exists between rivets from the two suppliers.

1. Use Excel’s Histogram option to create histograms for the original supplier and the new Supplier’s distribution of diameter measurements. Make sure you label each accordingly.

2. Use Excel’s descriptive statistics feature to provide a table of descriptive statistics.

3. The assumptions are:

a) The populations are normally distributed. Based on the histograms in part 1, this appears to be the case.

b) The populations have equal variances. The sample variance of the new supplier is about 3.5 time that of the original supplier. This assumption is likely not satisfied which means the students will have to adjust the degrees of freedom. Fortunately, Excel has an option to perform a test with unequal variances.

c) The sample are random. While this appears to be the case for the original supplier, nothing is mentioned in the case about the new supplier. However, the fact the sample distribution is approximately normal is evidence the sample is random.

4. Students will have to pick their own significance level.
And justify their choice.

5. Students could perform any of the three types of hypothesis test. The following is Excel output for a significance level of 0.02;
Students are encouraged to use a different significance for their analysis. Here the assumption is
UNEQUAL VARIANCES WITH ALPHA = 0.02

100

t-Test: Two-Sample Assuming Unequal Variance s																																	Alpha = 0.02
			Original Supplier		New Supplier
	Mean	0.3755	0.3750
	Variance	0.000113	0.000393 199
	Observations				100
	Hypothesized Mean Difference		0
	df	151
	t Stat	0.2223
	P(T<=t) one-tail	0.4122
	t Critical one-tail	2.0716
	P(T<=t) two-tail	0.8244
	t Critical two-tail	2.3513

Students can also do t-Test for Two Samples

Assuming Equal Variances
in Excel with the same significance level as they did with the assumption of unequal variances.

 

Original Supplier

New Supplier

Mean

Variance

Observations

100

100

Hypothesized Mean Difference

0

df

t Stat

P(T<=t) one-tail

t Critical one-tail

P(T<=t) two-tail

t Critical two-tail

 

t-Test: Two-Sample Assuming Equal Variances, Alpha = 0..05
0.37545	0.37495	-0.0005
0.000112836	0.000393	0.000280364
Pooled Variance	0.000253018
198
0.222269348
0.412166656
1.285841842
0.824333311
1.652585784

6. Students should present a well-organized report containing the output presented above.
Notice there is not a significant difference for either the one or two tailed test. Students should make the appropriate conclusions by comparing the critical values against the t-stat – one or two tailed test, or whether assuming equal or unequal variances.