SMU Business Statistical Difference in Annual Sales Questions

John has been running a number of small entrepreneurial businesses from his family farm. His side-hustle is producing honey and selling bottles at the farmer’s market. Over the past few years, sales of honey have been flat, which has actually led to reduced profitability since bees on the farm have been decreasing. This year John sought the help of DBA Business Consultants, LLC., in evaluating his product offerings in the hope of boosting sales. The consultant suggested that the sales of the honey could be boosted by new labeling. John decided to re-name and re-label the honey:  Queen Bee Magic Potion #9 Elixir. Total unit sales of honey are shown below for each location, in 2020 prior to the change of product marketing, and in 2021 after the new marketing initiative.  

2020 Sales in Jars             2021 Sales in Jars

Farmer’s Market                             85                                         140

Cranberry Days                               55                                         90

County Fair                                       42                                        75

Wool Festival                                   110                                      150

Firework Days                                  95                                        199

• 1)Using the data supplied above, design a test to determine if there has been a statistical difference in annual sales of honey. State your test design, hypothesis, and assessment criteria to accept or reject your hypothesis.  
• 2)Run your test, what do the results suggest? 
• 3)Can you attribute your results to the product re-naming? Why or why not? How could you know for sure? Discuss.

John has a second side-hustle for pies with a friend, Andy…..he owns a confection making machine (die) that will make mini-pie treats. The initial cost of the die is $850, and all other additional costs are $3.00 per unit produced. 

4) Express the total cost C (in dollars) as a linear function of the number of q units produced.

5) How many total units are produced if the total cost incurred is $1,600?

6) How would you design a study to assess if either or both the product re-marketing and/or mini-pie treats are financially viable products for Parker’s portfolio? Discuss.