**PROBLEM 1**

__Situation:__

Ska Brewing Company is a producer of fine craft beers located in Durango, Colorado. With its flagships Ale and Lager, they have enjoyed double-digit growth for more than a decade with no signs of allowing down.

Ska was founded in 1995, and through hard work and laser-like focus on brewing great beer continued to grow. In 2012, Ska brewed more than 25,000 barrels of beer (1 barrel = 2 standard kegs = 4,032 ounces) with sales exceeding $6.5 million.

__Action:__

Using the attached MS Excel Workbook, use the methods of descriptive statistics analytics to summarize the Ska ** annual data** listed in table 1. Discuss your findings.

- Include a summary of each variable (number of barrels sold and gross annual sales) in the data set. Use histograms, descriptive statistics, and Empirical rule to gain insight and detect data patterns. Your answer should refer to histograms, Empirical rule, and descriptive statistics (mean, median, mode, standard deviation, skewness, and kurtosis) to explain detected data patterns (i.e. increasing/decreasing/stable trends, whether the data is normally distributed based on Empirical rule, …).

**USING RED FONT SHOW YOUR ANSWER FOR PART a HERE.**

**THE FOLLOWING INSTRUCTIONS APPLY TO ALL SECTIONS OF THE CASE STUDY REPORT WHERE ANSWER TO QUESTION IS REQUIRED:**

**LABLE EACH EXCEL/MINITAB OUTPUT USED TO ANSWER EACH QUESTION AND PLACE THE TABLES/GRAPHS AT THE END OF THE REPORT IN THE “APPENDIX – EXCEL/MINITAB OUTPUT DATA”. SEE THE SAMPLE TABLE IN THE APPENDIX.****HERE IS WHAT A TYPICAL ANSWER COULD LOOK LIKE” BASED ON DESCRIPTIVE STATISTICS PROVIDED IN TABLE 1, THE MAXIMUM AND MINIUM AGE OF SUBSCRIBERS ARE 45 AND 22, RESPECTIVELY. FURTHERMORE, THE MEAN, MEDIAN, AND MODE FOR THE AGE OF THE SUBSCRIBERS ARE 33.2, 33, AND 32, RESPECTIVELY. THIS DATA SUGGESTS THAT DISTIBUTION OF THE DATA IS SYMMETRICAL. THIS IS ALSO SUPPORTED BY LOW SKEWNESS VALUE OF 0.16.”****USE “ENTER” KEY TO ADD MORE LINES IN THE ANSWER SECTIONS TO CREATE MORE SPACE FOR YOUR ANSWERS AS APPROPRIATE****DELETE THE ABOVE INSTRUCTIONS SHOWN IN RED FONT WHEN SUBMITTING YOUR CASE STUDY REPORT FOR GRADING. ONLY SHOW YOUR ANSWER FOR EACH QUESTION AS THE ABOVE INSTRUCTIONS ARE NOT NEEDED FOR GARDING CASE STUDY REPORTS.**

For the next two parts of this problem, use the descriptive statistics to summarize the Ska ** monthly data** listed in table

- Discuss your findings with respect to the
measures of central tendency (mean, median, and mode), measures of dispersion (range and standard deviation), skewness, and kurtosis of the data. Refer to Empirical rule as a part of interpretation of the monthly data patterns.__appropriate__

**USING RED FONT SHOW YOUR ANSWER FOR PART b HERE**

- One concern at Ska is seasonal variation. The brewery is much busier during summer months than during winter months. Two possible explanations for this phenomenon are that 1) people simply buy more beer during summer, and 2) Ska releases two very popular seasonal beers, Mexican Logger and Euphoria Pale Ale at the beginning and end of summer season. To get a better handle on the seasonal variation at Ska, your task is to draw clear picture of what’s happening (data visualization such as histogram and trend lines). Make sure to include in your answer, based on descriptive statistics, whether there appears to be seasonal variation present in the monthly number of barrels sold and monthly gross sales comparing warm summer months to cold winter months.

**USING RED FONT SHOW YOUR ANSWER FOR PART c HERE**

- For this part of problem, note that two pieces of data is provided, namely, number of barrels and monthly gross sales. Considering that there is obvious increasing trend in annual gross income, is this increase due to increase in number of barrels sold or price increase per barrel? Justify your answer based on descriptive statistics. Hint: you would need to calculate price per barrel based on gross income and number of barrels sold based on data provided.

**USING RED FONT SHOW YOUR ANSWER FOR PART d HERE**

Table 1.

**PROBLEM 2**

__Situation__

The price of a pound of tomatoes varies seasonally. Michael King, a store manager for a Kroger store in Detroit metro area, wants to price a pound of tomato competitively. He wants to use the price range for a pound of tomatoes in the Detroit metro area to price a pound of tomatoes for his store that he manages. He selects at random 39 stores in Detroit metro area and records the prices charged as shown below.

$1.32 | $1.45 | $1.20 | $1.10 | $0.99 | $1.65 | $1.99 | $1.18 | $1.59 | $1.68 | $1.43 | $1.00 | $1.29 |

$1.82 | $1.09 | $2.09 | $1.79 | $1.09 | $1.72 | $1.45 | $1.53 | $1.67 | $1.78 | $1.44 | $1.60 | $1.12 |

$1.39 | $1.45 | $1.78 | $1.11 | $1.18 | $2.00 | $1.00 | $0.99 | $1.45 | $1.62 | $1.45 | $1.39 | $1.89 |

Action

- Is the sample size of 39 adequate using confidence level of 99% to estimate the price of a pound of tomatoes so that the estimated cost is within $0.20 of cost charged by the stores in Detroit Metro area? Assume that the population standard deviation is $0.30. Justify your answer based minimum sample size equation/calculation.

**USING RED FONT SHOW YOUR ANSWER FOR PART a HERE**

- What is the 99% confidence interval range for price of a pound of tomatoes if the sample data above is used?

**USING RED FONT SHOW YOUR ANSWER FOR PART b HERE. YOU NEED TO SHOW THE UPPER AND LOWER LIMITS OF THE CONFIDENCE INTERVAL.**

- What is the 95% confidence interval range for price of a pound of tomatoes if the sample data above is used?

**USING RED FONT SHOW YOUR ANSWER FOR PART c HERE. YOU NEED TO SHOW THE UPPER AND LOWER LIMITS OF THE CONFIDENCE INTERVAL.**

- What is the 90% confidence interval range for price of a pound of tomatoes if the sample data above is used?

**USING RED FONT SHOW YOUR ANSWER FOR PART d HERE. YOU NEED TO SHOW THE UPPER AND LOWER LIMITS OF THE CONFIDENCE INTERVAL.**

- Review the results from part b, c, and d and explain what happens to the range of the intervals? Answer this question in context of whether the range is getting wider or narrower as the confidence level is changed. Do the results make sense? Explain why, or why not.

**USING RED FONT SHOW YOUR ANSWER FOR PART e HERE. MAKE SURE TO ADDRESS THE PART OF THE QUESTION RELATED TO “**Do the results make sense? Explain why, or why not.”

- Describe what is precision. Next, comment on precision of the confidence intervals computed in part b, c, and d. Answer this question with respect to which of the three confidence intervals computed in part b, c, and d has a higher precision and why.

**USING RED FONT SHOW YOUR ANSWER FOR PART f HERE. **

- Based on the confidence interval computed in part b, if the decision maker wants to maintain the same confidence level, i.e. 99%, however, it is desired to improve the precision of this confidence interval, what option the decision maker has to improve the precision and still maintain the same confidence level?

**USING RED FONT SHOW YOUR ANSWER FOR PART g HERE**

**PROBLEM 3**

__Situation:__

Many people believe that there is a “Friday effect” in the stock market. They do not necessarily spell out exactly what they mean by this, but there is a sense that the stock prices tend to be lower on Fridays than on Mondays.

__Action:__

Because stock prices are readily available on the web, it should be easy to test this hypothesis empirically.

- Before collecting data and running test, however, you must decide exactly which hypotheses you want to test because there are several possibilities. Formulate two sets of null/alternative hypotheses: a two-tail test of hypothesis to determine if the prices are different on Fridays versus Mondays and a one-tail test of hypothesis to determine whether Friday prices are lower than Monday prices .

**USING RED FONT SHOW YOUR ANSWER FOR PART 1 HERE SHOWING BOTH SETS OF TEST OF HYPOTHESES.**

- Decide on criteria to support or refute your hypothesis. Specify significance level (0.01, 0.05, 0.1).

**USING RED FONT SHOW YOUR ANSWER FOR PART 2 HERE**

- Collect a year’s worth of data points (52 Fridays and the following Mondays) from the stock market and perform the 2 Sample T – test analysis.

**USING RED FONT SHOW YOUR ANSWER FOR PART 3 HERE**

- What are the p-values for the two sets of test of hypotheses? State whether the null hypotheses are rejected or not for each test.

**USING RED FONT SHOW YOUR ANSWER FOR PART 4 HERE**

- Can you conclude that there is a statistically significant Friday effect in the stock market based on the two sets of tests of hypothesis conducted? Explain in detail.

**USING RED FONT SHOW YOUR ANSWER FOR PART 5 HERE**

**PROBLEM 4**

A new software package is being developed and tested to help analysts reduce the time required to design, develop, and implement a new information system. To evaluate the benefits of the new software package, a random sample of 24 systems analysts is selected. Each analyst is given specifications for the new information system. Twelve analysts are instructed to produce the information system by using current technology. The other 12 analysts are trained in the use of the new software package to be used to produce the information system. The following data represent the completion times:

Current Technology | New Software |

300 | 274 |

280 | 220 |

344 | 308 |

385 | 336 |

372 | 198 |

360 | 300 |

288 | 315 |

321 | 258 |

376 | 318 |

290 | 310 |

301 | 332 |

283 | 263 |

Using a .025 level of significance, test whether the current technology took longer than the new software to complete the project. Show the following in your report:

- Ho & Ha

**USING RED FONT SHOW YOUR ANSWER FOR PART 1 HERE**

- p-value

**USING RED FONT SHOW YOUR ANSWER FOR PART 1 HERE**

- Reject/don’t reject Ho based on comparison of p-value to alpha.

**USING RED FONT SHOW YOUR ANSWER FOR PART 1 HERE**

- Your conclusion, specific to the problem statement with respect to whether the new software should be replacing the current technology

**USING RED FONT SHOW YOUR ANSWER FOR PART 1 HERE**

**APPENDIX – EXCEL/MINITAB OUTPUT DATA**

**MICROSOFT ‘SNIPPING TOOL’ WAS USED TO CREATE THE IMAGES FOR THE TWO TABLES SHOWN BELOW. FOR MORE INFORMATION ON HOW TO USE ‘SNIPPING TOOL’, PLEASE DO A GOOGLE SEARCH ON ‘SNIPPING TOOL FOR MAC’ OR ‘SNIPPING TOOL FOR WINDOWS’. CLICK ON THE IMAGES AND DRAG THE LOWER RIGHT CORNER TO CHANGE THE SIZE OF THE IMAGES. DELETE BELOW IMAGES WHEN SUBMITTING YOUR CASE STUDY ASSIGNMENT FOR GRADING AS THESE IMAGES ARE FOR REFERENCE.**

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