Understanding Business Drivers and Improving Business Forecasts

Use Common Statistical Tests to Draw Conclusions From Data Reeshemah Simmons

Applied Managerial Decision-Making

MGMT600-2001A-03

January 29, 2020

Introduction: The situation

Big D is company that is considering expansion into a new market in Chicago needs some data backed reasons to do so. The company wants to diversify as it expands into the new market and this diversification is done justified by various previous projects. The factors considered for diversification include population, household income, per capita income, race and ethnicity, educational attainment, and means of transport for the working class. The company has observed that in Chicago, there is high rate of educational attainment, and thus the targeted market is able to appreciate the market and understand the functions of their products. In addition, the company can enjoy the benefits of a well-educated populace because it will get people who are skilled and have experience to employ.

With regard to the population, Big D will enjoy an increasing market size in the long-term if the trends from 1980 is to go by. Big D stands a good future of the market as the population continues to grow. Median household income shows rather a similar trend. The median household income for Chicago is even higher than that of the entire country. As the company plans to expand to this state, the median household income supports its move. This shows that Chicago is potential market for Big D. Another important factor of consideration for Big D and that supports its quest for expansion into Chicago is the high per capita income. If the products target a certain race, the White race has increasingly grown for the 20 years in consideration. Big D thus would use this information to develop or produce products that target the white race. The means of transport to work also point to a populations demand for products. Given the high number of people who drive to work, Big D stands a chance to grow its market in the area.

Scenario

The end goal pf Big D is to expand its market into other states and towns in the US. It is the desire of every company to expand into markets that have potential for growth. As such, Big D carried out some analysis of the population in Chicago and that of the US in consideration of certain factors. One of its strategies is to consider markets that promise growth for the future. Selling outdoor sporting goods in Chicago seems to be a noble undertaking for the company. As the company looks for a new market to expand to, the factor under consideration are in favor of Big D expanding to Chicago.

However, it is important to carry out other analyses to support this observation from the previous analysis. One way to do this is the use of Chi-square Test. Chi-square test will provide statistical evidence to help in making the decisions that the company need to make.

Chi-Square Test

The test is a distribution-free test and it is applicable in given conditions. One of these conditions is that the variables ought to be measurable in an ordinal or nominal scale. In addition, it is used in equal and unequal sample sizes (Bozeman, 2011). However, there in certain cases, some non-parametric tests can only be used with equal sample sizes. The data to be used does not follow normality assumption.

Assumptions for Chi-Square test

There are certain assumptions of Chi-Square tests that are applicable in this case. One of the assumptions is that the data involved has frequencies and counts only. No percentages. Further, the categories being studies are mutually exclusive (McHugh, 2013).

Chi-Square tool for Big D

This test requires the identification of two related variables. Since it is used in categorical and nominal data, the chi-square test of independence considers the association that exists between the variables. For Big D, it will be used to check the relationship of the variables under the study or to identify whether they were independent of each other.

Hypothesis for Chi-Square

Null hypothesis : There exists no difference between frequencies of indoor sporting production and outdoor sporting production

Alternative Hypothesis : There exists a significant different between frequencies of indoor sporting production and outdoor sporting production

Since all the data that is needed for the core competencies of the business are not provided, using the essential factors needed for Big D expansion.

The data to use with regard to the expected frequencies of the factors under consideration for expansion is income. This is income by type. In this case, observed counts represent US while expected is for Chicago.

Income by type: Earnings	Observed	Expected
$ 1 to $2,499 or less	10,621,378	1,991
$ 2,500 to $4,999	7,953,137	1,875
$ 5,000 to $7,499	8,124,698	1,564
$ 7,500 to $9,999	6,504,581	775
$ 10,000 to $12,499	9,597,527	1,579
$ 12,500 to $14,999	6,201,326	743
$ 15,000 to $17,499	8,302,907	1,222
$ 17,500 to $19,999	6,179,510	861
$ 20,000 to $22,499	9,086,198	1,516
$ 22,500 to $24,999	5,644,521	659
$ 25,000 to $29,999	12,996,782	2,716
$ 30,000 to $34,999	11,366,211	2,868
$ 35,000 to $39,999	9,219,670	2,937
$ 40,000 to $44,999	7,744,095	3,348
$ 45,000 to $49,999	5,200,969	2,627
$ 50,000 to $54,999	5,563,669	2,875
$ 55,000 to $64,999	6,146,281	3,727
$ 65,000 to $74,999	2,041,290	2,520
$ 75,000 to $99,999	2,191,536	3,967
$100,000 or more	1,850,632	5,536
Total	142,536,918	45,906
CHITEST
0.000

p-value = 0.000. It is less than 0.05 and this shows a strong evidence for rejecting the null hypothesis. Therefore we reject the null hypothesis. We conclude that there exists a significant different between frequencies of indoor sporting production and outdoor sporting production. There is a difference between the expected and the observed data.

Conclusion

Big D is in need of expansion and development into new areas. The consideration of different factors and elements pertaining to the market presents a possibility to analyze the market in terms of its potential. The company has established that Chicago has a large population, the households have increasing income, there is a large number of people with undergraduate and graduate education and that its race composition is predominantly white. Chi-square test is conducted to ascertain if the move to expand is backed by this data. Coming from a null hypothesis that producing indoor sporting products and producing outdoor sporting products is not different, the results favors rejecting of the null hypothesis (Franke, Ho, Christie, 2011). This is backed by the p-value obtained from CHITEST of 0.000 which is smaller than the required > 0.05. Since the median household income and per capita income in Chicago are higher in Chicago than in US, Big D should expand its outdoor sporting products to Chicago. This presents a better chance for the business to expand and grow since the targeted market have high rates of per capita income.

References Bozeman Science. (2011, November 13). Chi-squared test [Video file]. Retrieved from YouTube: https://www.youtube.com/watch?v=WXPBoFDqNVk Franke, T. M., Ho, T., Christie, C. A. (2011). The Chi-square test: often used and more often misinterpreted. American Journal of Evaluation, 33(3), 448-458. McHugh, M. L. (2013). The Chi-square test of independence. Biochemia Medica, 143-149.