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Random Sampling, Confidence Intervals, and Hypothesis Testing


Writing Guidelines


Quant_Assign03_data.xls and Quant_Assign03_Examples.xls goes with this assignment.

Kane Suppliers, Inc.

You are the general manager for an Eastern Corn Belt input supplier, Kane Suppliers, Inc.  Currently, your company supplies agricultural chemicals, fertilizer, and seed to farmers in the Eastern Corn Belt. The Board of Directors for your company has expressed interest in expanding the company.  You and the management team are considering expansion to the Western Corn Belt.  However, much uncertainty remains about farmers’ profiles in the Western Corn Belt compared to the ones in the Eastern Corn Belt.  You have been asked to obtain data on farmers’ profile for both areas. Your objective is to determine if farmers in the Western Corn Belt would be receptive to your company’s business model, which focuses on delivering high quality service with a slight price premium.

To answer the question concerning farmers’ receptiveness to your business model, you have obtained data from the Large Commercial Producer survey developed every 5 years by the Center for Food and Agricultural Business at Purdue University. The data you received are responses to the question: “when you choose a supplier for expendable items such as pesticides or feed, how is your decision influenced by price on a scale of 0 to 100%?”  If the farmer chooses 100%, for example, then they are saying that their purchasing decision is entirely driven by the price of the product and it would be unlikely that your business model would work well for that farmer (higher price, with higher service). You have 32 observations available for the Western and Eastern Corn Belts.

Consider each of the following questions in preparing your two-page memo to the Board of Directors.  Be sure to explain the relevance of the following questions in your memo.  Remember, the members of the Board of Directors have little knowledge of statistics, so be sure to explain what the numbers mean in a simple manner.  Properly label all charts, graphs, and tables and report all numbers to two decimals. It is not necessary, however, to apply the two decimal place rule to your graphs.

Part A – Chapter 8 – Lecture 3a

  1. Calculate the mean for the weight farmers place on price as a factor in their purchase decision for both the Western and Eastern Corn Belts. Interpret these values.
  2. Calculate the standard deviation for the weight farmers place on price as a factor in their purchase decision for the Western and Eastern Corn Belts.  Interpret.
  3. Calculate the standard error for the mean weight farmers place on price as a factor in their purchase decision for the Western and Eastern Corn Belts.  Interpret.

Part B – Chapter 9 – Lecture 3b

  1. Calculate a two-sided confidence interval for the mean weight farmers place on price as a factor in their purchasing decision for the Western and Eastern Corn Belts.
  2. Is it possible that the “true” mean weight placed on price as a factor in the purchase decision in either or both regions could be 20%?  How can you tell?
  3. For both regions, calculate a one-sided confidence interval for “at least as great as.”  Interpret.
  4. For both belts, calculate a one-sided confidence interval for “no larger than.”  Interpret.

To properly answer Part B, you must select a significance/confidence level.  In your memo, be sure to justify why you chose the significance/confidence level that you did. 

Part C – Chapter 10 – Lecture 3c

  1. Test the hypothesis that the mean weight placed on price as a factor in the farmers’ purchasing decision is equal 25% for the Western and Eastern Corn Belts.  Test each region separately.
  2. Test the hypothesis that the mean weight placed on price as a factor in the farmers’ purchasing decisions for the Western and Eastern Corn Belt is less than or equal to 20%.
  3. Test the hypothesis that the mean weight placed on price as a factor in the farmers’ purchasing decision for the Eastern Corn Belt is greater than or equal to 30%. 
  4. Test the hypothesis that no difference exists in the percentages between the Eastern and Western Corn Belts.  Assume equal variances.

To answer Part C, you must again select a significance level.  Justify why you chose the significance level that you did.

Bonus Question:  You may do this on a separate page that does not count toward the 2-page limit.

Your Vice President of Marketing argues that the true test of whether the model will work is how the farmers rank the importance of price relative to the importance of service.  That is, as long as the relative weights for price and service are the same in the Eastern and Western Corn Belt, she argues that your business model would likely work.  Your dataset contains each farmer’s ranking of service as well as their ranking for price (The data for price and service is paired for each region but not across regions).  Based on the Vice President’s argument, conduct a hypothesis test of the relative difference in each region.  Based on the results of this test would you change your recommendation? 


Grading Rubric


Assignment 3 Rubric
CriteriaRatingsPts
This criterion is linked to a Learning OutcomeRecommendation for the board15.0 pts Recommendation is given that is consistent with the interpretation of the data and is the first sentence of the memo 12.0 pts Recommendation is given that is consistent with the interpretation of the data and is in the first paragraph 9.0 pts Recommendation is given that is consistent with the interpretation of the data 5.0 pts Recommendation is given that is not consistent with the interpretation of the data 0.0 pts No recommendation is give15.0 pts
This criterion is linked to a Learning OutcomeMean and variability20.0 pts Level 4 plus a graph or figure is used to illustrate the findings 15.0 pts Mean and variability are correctly calculated and interpreted in a manner that informs the board’s decision making 10.0 pts Mean and variability are correctly calculated, but poorly interpreted 5.0 pts Mean and variability are incorrectly calculated and interpreted 0.0 pts Mean and variability are not addressed in the memo20.0 pts
This criterion is linked to a Learning OutcomeConfidence Intervals20.0 pts Level 4 plus a graph or figure is used to illustrate the findings and the significance level is well justified 15.0 pts Confidence intervals are correctly calculated and interpreted in a manner that informs the board’s decision making 10.0 pts Confidence intervals are correctly calculated, but poorly interpreted 5.0 pts Confidence intervals are incorrectly calculated and interpreted 0.0 pts Confidence intervals are not addressed in the memo20.0 pts
This criterion is linked to a Learning OutcomeHypothesis Tests20.0 pts Level 4 plus a graph or figure is used to illustrate the findings 15.0 pts Statistics related to hypothesis tests are correctly calculated, but poorly interpreted Statistics related to hypothesis tests are correctly calculated and interpreted in a manner that informs the board’s decision making 10.0 pts Statistics related to hypothesis tests are correctly calculated, but poorly interpreted 5.0 pts Statistics related to hypothesis tests are incorrectly calculated and interpreted 0.0 pts Hypothesis tests are not addressed in the memo20.0 pts
This criterion is linked to a Learning OutcomeGrammar10.0 pts Level 4 and pronoun use is correct 7.0 pts Level 3 and no grammatical errors 4.0 pts No spelling errors, but some grammatical errors 2.0 pts No spell check errors, but spelling errors exist 0.0 pts Several spell check errors10.0 pts
This criterion is linked to a Learning OutcomeReadability15.0 pts Level 4 and graphs and tables are well labeled 12.0 pts Level 3 and memo uses headings to guide the reader, and graphs, figures and tables to illustrate key points 9.0 pts Memo uses paragraphs and simple sentences. Language is appropriate for someone who understands very little about hypothesis testing 5.0 pts Memo uses paragraphs, but sentences often contain several thoughts 0.0 pts Memo is one giant run on sentence15.0 pts
Total Points: 100.0
  

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