Statical Data in a Business

A Decision of Uncertainty

This document will familiarize you with the expectations of this assignment and provide some direction on how to structure it. This material is an example only, as you must research statistical data to help make a business decision. The concepts that follow focus on a personal decision of uncertainty. Use these probability concepts to guide you in structuring your assignment. Remember to present your paper as a narrative.

Assignment: A Decision of Uncertainty

Research statistical data within a business context that requires a decision to be made. Then, use probability on your researched data to formulate a decision.
Write a 650 -word paper in APA format(include introduction and conclusion) explaining your research methods and process for limiting the uncertainty within the decision. Discuss your results in an in-depth narrative. Be sure to explain the following in your paper:

The method you used to apply the concepts from the example scenario to formulate your business decision of uncertainty
The appropriate probability concepts and your application of them to find data that limited the uncertainty of this business decision
Identifications of each discrete outcome from your statistical analysis, providing a statistical rationale for each
The trade-offs between accuracy and precision required by the use of various probability concepts and the effect on your data

Example Scenario: To Buy or Not to Buy Cruise Insurance

I decided to take a cruise this year. Due to money and work constraints, the cruise was during the month of October. Through my research and in compliance with my constraints, the most opportune time to travel on a cruise was from October 8 through October 14. However, according to the weather bureau, this particular week was the height of hurricane season.

According to the cruise line, there is no refund if a cruise is cancelled due to a hurricane. However, hurricane insurance can be purchased for a fee of 30% of the original ticket price. The insurance will refund the ticket money but not the fee if the cruise is cancelled.

I have to decide whether to book the cruise and not worry about hurricanes,which risksthe loss of my vacation fund, or book the cruise and pay extra for the hurricane insurance, which subsequently adds more to my costs and stresses the allocated budget for this vacation.

Research

To make an accurate decision, I researched my trip. My researched data set was from the National Oceanographic and Atmospheric Administration (NOAA) and consisted of weather condition statistics over the past 10 years. More importantly, my research specified the date and duration of hurricanes. Since my trip was to take place from October 8 through October 14, my research primarily concentrated on this period.

Once the research was gathered, I focused on accurately interpreting my data to make an accurate decision.

Interpretation of Data (using Bayes’ Theorem)

To interpret my data, I chose to use Bayes’ theorem as the probability model that was the most applicable to my vacation decision. Bayes’ theorem emulates the process of logical inference by determining the degree of confidence in possible conclusions on the basis of available evidence. This evidence is best stated in terms of subjective probability, where probability is assigned based on the outcome of the evaluation of opinions and information and the estimation ofavailable data, and finally assigning probability to the outcomes. Therefore, Bayes’ theorem can be used for the purposes of predicting confidence levels for purchasing hurricane insurance, predicting the occurrence of a hurricane, or predicting a captain’s cancellation notice if a hurricane occurs.

While there are other effective analytical tools used to derive the probability of data, such as hypothesis testing, Bayes’ theorem is more appropriate for this situation due to the subjective nature of the evidence. Part of statistical modeling is using the right analytical tool for the appropriate situation. Hypothesis testing is more effective for a scenario with an observed difference. In other words, hypothesis testing is used to determine the probability when a given hypothesis is true. In our cruise scenario, hypothesis testing could be used if one professional body said the probability of a hurricane occurring is .5 while another body stated that the probability of a hurricane occurring is .35. Since our variables are not defined, it is more effective to use Bayes’ theorem.

With the appropriate theorem chosen, I continued to gather my data.

After contacting the cruise line, I found that 5% of Caribbean cruises during hurricane season are cancelled by harsh weather conditions.

I then set up the variables to examine the probability of cancellation.

Cruise 1 = C1 = cancelled by hurricane
Cruise 2 = C2 = not cancelled by hurricane

In turn, this helped me decide whether I should buy hurricane insurance.

The following is a list of what I knew:

The dates of the cruise are already determined (October 8–14)
The probability of our cruise being canceled by a hurricane is 5%; (P(C1) = cancelled by hurricane = .05).

So, the prior probability of the cruise remainingunaffected is P(C2) = .95

The weather bureau’s historical evidence cross-referenced with the cruise line’s schedule (October 8–14) showed that if there is a hurricane in the area there was a 90% chance the cruise would be cancelled. In other words, B = hurricane is present (as indicated by the weather bureau). This is written as P(B|C1) = .90.

The cruise line additionally stated that even though a hurricane may surface, cancellation is not always imminent. Cancellation also depends on the subjective nature of the captain’s opinion.

The probability of the cruise being not being cancelled due to bad weather is 15%, written as P(B|C2) = .15.

Posterior probability according to Bayes’ shows us:

P(C1/B)=(P(C1)P(B¦C1))/(P(C1)P(B¦C1)+P(C2)P(B¦C2) )

=(.05)(.9)/((.05)(.9)+(.95)(.15) )=(.045)/(.1875)= .24

According to the calculations, the data illustrates the probability that the cruise will be cancelled at .24, provided that the weather bureau positively identifies a hurricane in the area.

The cruise line stated that if a cruise is selected at random during hurricane season, the probability that it will be cancelled is .05. Now, if the weather service states a hurricane is in the area, the probability for cancellation rises from .05 to .24

It is important to plug the data into a table to check for accuracy and help determine what decision to make.

Event Prior Probability
P(Ci) Conditional Probability
P(B|Ci) Joint Probability
P(Ai and B) Posterior Probability
P(Ai|B)
Cruise Cancelled .05 .90 .0450 .0450/.1875 = .24
Cruise not Cancelled .95 .15 .1425 .1425/.1875 = .76
P(B) = .1875 = 1.00

According to the above calculations, there is a .24 probability that the cruise will be cancelled and a .76 probability that the cruise will go as planned.

Decision

All of our decisions involve risk and our own personal tolerance for risk. Statistical tools for analyzing data give us a means of minimizing that risk. On the basis of the above analysis of available data, what would you do? Would you book the cruise, not worry about hurricanes, and risk losing your vacation fund? Would you book the cruise and pay extra for the hurricane insurance, which adds to your spending and stresses the allocated budget for this vacation?
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