Homework assignment

Applying Statistical Techniques for Big D Incorporated Outdoor Sporting Goods Expansion

MGMT600-1801B-03

Applied Managerial Decision-Making

Unit 3 IP

Instructor: Dr. Charlotte Scott

Colorado Technical University Online

3/7/18

Tina L. Davis

Contents Executive Summary 3 Chi-Square Distribution Tool 4 Hypothesis Testing 5 Two Other Nonparametric Tests 6 Conclusion 7 References 8

Up to this point, from Phase 1 and Phase II, Big D Incorporated has reviewed data regarding the outdoor sporting goods expansion for their client. In the first phase, differentiation of qualitative and quantitative data was demonstrated, utilizing several examples. Additionally, in Phase 1, campers and sports teams were the two populations identified for this study. In the second phase, the 2000 U.S. Census specific comparisons with Chicago 60614 (the area the client would like to launch outdoor sporting goods products) were evaluated and impressive results were gathered. This report explores the application of Chi-Square Distribution Tool, hypothesis testing, and nonparametric testing. These statistical techniques will be explained and their relativity to how helpful they are to this business decision-making process, (CTU, 2018).

As the Business Analyst, it is essential to employ the necessary statistical tools and techniques in the business decision-making process. Big D Incorporated has been entrusted with the responsibility of making adequate recommendations that will successfully launch the outdoor sporting goods product offerings that their client so desires to implement, (CTU, 2018). Should the client expand or keep their current position? Statistical tests such as Chi-Square Distribution Tool, hypothesis testing, and nonparametric testing are some of the methods that can aid in answering tough business decisions such as this.

In 1876, Friedrich Robert Helmert of the Kingdom of Saxony (this area was part of the German Empire) was the first to introduce chi-square distribution, but the first chi-squared test was utilized by Karl Pearson in 1900, (Research Optimus, 2018). The chi-square distribution is known to be deployed by chi-square tests as a way of inspection between “observed value and expected value,” (Chiu, 2016). In other words, the role of chi-square is to aid in identifying how two variables are related to one another & assess the “independence of two variables,” (Deshpande, 2011). Chi-square distribution is widely utilized in inferential statistics primarily for making an inference of a population often using categorical data & it is considered to be nonparametric in nature (meaning the population that is being sampled does not have to meet specific criteria or “assumptions”), (Investopedia, 2018). Chi-square distribution is the “distribution of the sum of squared standard normal deviates where the degree of freedom is equal to the number of standard normal deviates being summed,” (Scott, 2018). For example, if surveys were distributed to a sample of the population identified that go camping on a regular basis (keep in mind that in Phase 1, campers & sports teams is the population being studied in this research) and Big D Incorporated wanted to find out the “90 percent confidence interval for the variance and standard deviation” for the price spent in camping sporting goods for randomly selected families and the “variable is normally distributed,” chi-square distribution tool can be applied in discovering this data, (Duvvuri & Singhal, 2016). The chi-square statistic is:

(Intellipath., 2018). So the mean and the variance of the sample would be calculated as well as the standard deviation and the degree of freedom, (Duvvuri & Singhal, 2016). A computer program can be used or the critical values table to compute chi-square value, (Duvvuri & Singhal, 2016). Moreover, hypotheses testing is another statistical tool in business decision-making.

Hypothesis testing is highly essential in the business decision-making process. It is an opportunity for the analyst to test an assumption regarding sample data of a population (in the case of Big D Incorporated: campers and sports teams), (Investopedia, 2018). The steps of hypothesis testing are as follows:

1. That the hypothesis: one is positive and the other one is negative,

2. Determine how the data will be assessed,

3. Evaluate the sample data, and

4. Accept or reject the null hypothesis based upon the results, (Investopedia, 2018).

As the business analyst, the proposed hypothesis is:

H1: Sports teams (in Chicago 60614) will purchase a higher percentage of outdoor sporting goods than families (in Chicago 60614) that go camping regularly.

H0: Sports teams (in Chicago 60614) will not purchase a higher percentage of outdoor sporting goods than families (in Chicago 60614) that go camping regularly.

The difference between the null hypothesis and the alternative hypothesis is shown in the chart below:

There are several nonparametric tests, but two are discussed here are the “Mann-Whitney test and Mood’s Median test,” (Statistics How To, 2018). The Mann-Whitney test would be instrumental in this study due to its ability to compare two populations (campers vs. sports teams), (Statistics How To, 2018). The test makes no suppositions about the “distribution of the population” and this method can be used to measure small or large samples, (Statistics How To, 2018). The Mood’s Median methodology tests the comparisons of the “median” from two samples to determine their differences, (Statistics How To, 2018). The business analyst for Big Data Incorporated felt these two techniques would unveil and delve deeper into the data, the profitability potential of our sample population of campers and sports teams.

In summation of chi-square distribution, hypothesis testing, and nonparametric testing each of these methods conclude that sport teams produce a higher percentage of outdoor sporting goods purchases because there is an array of sports teams in Chicago. Middle school, high school, college (public & private institutions), professional sports teams, numerous churches that have teams, the YMCA, Upward Bound programs, private organizations, & families (family reunion team sports & activities) tallied at an astronomically higher degree on the sample (using surveys) than families that camp out on a continually basis. However, the research continues to affirm if launching outdoor sporting goods in the Chicago area only will be substantial enough to be profitable for many years to come. The upcoming report on multivariate techniques can reveal additional information helpful for the final decision of the client of Big D Incorporated.

Chiu, D. (2016). Data science cookbook. Retrieved from http://proquestcombo.safaribooksonline

.com.proxy.cecybrary.com/book/programming/r/9781784390815.

CTU. (2018). Use common statistical tests to draw conclusions from data. Retrieved from https://

studentlogin.coloradotech.edu/UnifiedPortal/3/6#/class/150815/assignment/1104737.

Deshpande, B. (2011). How to use chi-square test for 3 common business analytics problems.

Retrieved from http://www.simafore.com/blog/bid/54594/How-to-use-Chi-Square-test

-for-3-common-business-analytics-problems.

Duvvuri, S. & Singhal, B. (2016). Spark for data science. Retrieved from http://proquestcombo

.safaribooksonline.com.proxy.cecybrary.com/book/programming/machine-learning/

9781785885655.

CTU. (2018). Intellipath III: nonparametric statistics. Retrieved from https://studentlogin.

Coloradotech.edu/UnifiedPortal/3/6#/class/150815/assignment/1104738.

Investopedia. (2018). Hypothesis testing. Retrieved from https://www.investopedia.com/terms

/h/hypothesistesting.asp.

Investopedia. (2018). Nonparametric method. Retrieved from https://www.investopedia.com/

terms/n/nonparametric-method.asp.

Mohan, R. PhD. (2016). Hypothesis testing can improve your business. Retrieved from

https://www.accenture.com/us-en/blogs/blogs-hypothesis-testing-improve-business-

decisions.

Research Optimus. (2018). What is chi-square? Retrieved from https://www.researchoptimus

.com/article/what-is-chi-square.php.

Scott, C. PhD. (2018). Chi-square distribution. {Live Chat #4}. Retrieved from https://student

login.coloradotech.edu/UnifiedPortal/3/6#/class/150815/livechat.

Statistics How To. (2018). Non parametric data and tests. Retrieved from

http://www.statisticshowto.com/parametric-and-non-parametric-data/.

Surbhi, S. (2016). Difference between null and alternative hypothesis. Retrieved from

https://keydifferences.com/difference-between-null-and-alternative-hypothesis.html.