Homework Assignment

Executive Summary

Based on the prior decisions to expand, Big D needs to consider all aspects that will contribute to its growth. It is therefore important to conduct the qualitative nonparametric test to demonstrate the position of the company in its expansion strategy. The needs to the company to expand is for diversification. The company decided to expand sits business to Chicago due to the existing opportunities. The previous report concluded that sport teams produce a higher percentage of outdoor sporting goods purchases because there is an array of sports teams in Chicago. We have observed that there is an opportunity for growth. Various factors will have an impact on the expansion strategy. This include the education rate, the population, ethnicity and also gender. The per capital income, labor force and employment rate are also significant factors in the expansion strategy. Opportunities identified in the new market include high employment, high consumption, high purchasing power and product awareness. The current goal of the company is to survive amid the high competition the company will face in new markets. The company also expects to innovate and change its culture in order to chive the business objectives. To make effective decisions, Big D needs to use the chi-square test to get useful statistical evidence. Big D also needs to use the qualitative nonparametric tests to understand its position in regards to the expansion strategy

Qualitative non-parametric test

It is important to first understand the nonparametric tests. Basically they are the tests that needs little or no assumption in regards to population distribution. It is useful in the cases where the dependent variable is nominal or ordinal, when there is an issue of normality to variance consistency and if the dependent variable distribution is partial (Mertler, 2016). The test is therefore important in making decisions and helping in analyses that use the median. The test is very accurate even if the used sample size is small.

To use the nonparametric test, we should execute various steps. Since they need little to no assumption of population parameters, we will not make any assumptions about the standard deviation or the mean of the population. The null hypothesis is equal. The first steep will be to establish a hypothesis and determine the level of significance (Mertler, 2016). For example, Big D wants to expand into the new market for their outdoor sporting goods. This will be successful because its brand is the best in the market. The alternative hypothesis will be equal to what we seek to prove. The null hypothesis will conflict the alternative hypothesis. The level of significance will be the likelihood of an incorrect decisions. It will involve the risk or likelihood of rejected.

Alternative hypothesis

Big D’s outdoor sporting goods are the best in the market.

Null Hypothesis

Big D’s outdoor sporting goods are not the best in the market.

The second step will be to establish the test statistic. This will involve obtaining the average number of the outdoor sporting goods sold in Chicago’s new market and use the average to determine the amount that should be sold. The forth step will be to establish the decision rule. This will include the statement that provides when to reject the hypothesis. The third step will be to compute the test statistic and analyze it and then compare it to the decision rule. Based on this comparisons, the null hypothesis will be accepted to reject. This means we shall draw conclusions from the findings.

Limitations of the Non parametric tests

Non parametric tests also have their limitation. When observations are ranked or nominal, measured imprecisely or subject to outliers, they become the perfect test to use. This is because in this instance the data will be difficult to analyze using the parametric methods without major assumptions regarding their distributions. However, the non-parametric method will lack power compared to many approaches of data analysis. This is especially when there is a small sample size. It is also common when the assumptions needed of the normality of data used is essential. The non-parametric tests are important in hypothesis testing and not in estimation (Naghettini, 2016). This makes them the best for our case. However, it is also possible to get estimates from the parametric tests and their confidence level but this is usually not straightforward

Another limitation is that the non-parametric test is not specified but rather determined from data. The name parametric means that the nature and number of parameters in the test are not fixed. They make no assumption about the size of the sample even in the event that the data observed is quantitative. It is useful of the data does not need ranking of the sorts. It is therefore important for qualitative data. Another limitation is that they have a low degree of confidence compared to results from a parametric tests. Therefore they may be less efficient in some cases.

Chi-Square Distribution tool

To help make a decisions, the chi square distribution tool will be important. The chi square test is a non-parametric test that is used under given conditions. The variables needs to be measure on an ordinal or nominal scale. The data under observation should violate the normality assumption. It is also appropriate for equal and unequal sample sizes although some non-parametric test will only address the equal sample size.

Chi-Square Distribution tool Assumptions

The assumptions for the chi square test include

· Chi-square tests deals with frequencies and counts

· The variables should be mutually exclusives

· Each matter can subsidize data to one cell in the x2

Chi-Square Distribution tool for Big D

The chi square test of independence is the statistical tool that is mainly used in identifying two related variables (Naghettini, 2017). In regards to categorical and nominal data, the test will address the association between variabkes. In business, the test will be of importance in exmaning how the variables under study are independing from each other or how they are related (Bozeman Science, 2011).

Chi-Square Hypothesis

Null Hypothesis:

There is no significant difference between outdoor sporting goods production in US and Chicago.

Alternative Hypothesis:

There is a significant difference between outdoor sporting goods production in US and Chicago

There is no adequate data to formulate a full Chi-Square for the outdoor sporting goods client. However, we have sufficient data to initiate this process. This nclude data such as the per cpaita income in chicago, the purching power as wll as the population. The analysis utilizes the essental data that may impact the exmapnsion of the business. In this case, we should use income of the population and compare to observed sales in the U.S to those expected in Chicago.

Based on the collected data. The p-value obtained is 0.0000. This value is less than 0.05. this means that ther is a strOng evidence for us to reject the null hypothesis. Therfore, we can conlude that there is a signficant difference in the number of sporting goods clients in U.S and number of sporting goods clients in chicago.

Limitations of the Chi-Square Distribution tool

Like other tools of analysis, the chi-square also has its limitations. First, the tool requires that all the participants that are measured in the analysis should be independent. This means that it is not possible for one to fit 2 or more categories. Only one category should be fit in. in the event that a participant fits in two categories, the chi-square analysis becomes inappropriate.

Another limitation us that the data used must be frequency data. For example, in our case if we are just measuring if the outdoor sporting goods are on demand, the chi square become appropriate (Naghettini, 2016). This is because we shall be calculating the expected clients to purchase the outdoor sporting goods. Since our research was based on income categories and there were more than 5 expected clients, the chi square becomes more appropriate. The chi square also requires a high sample size which is not less than 50. In our cases, the sample size was more than 50 making it appropriate.

Conclusion

Big D decide to expand and grow its business in Chicago. Various factors will impact the outcomes of this decision, this include the population, per capita income and employment rate in Chicago. To justify the decision farther, the chi-square distribution tool was utilized. The initial steps of qualitative nonparametric tests were also demonstrated. From these analysis, the board of directors need to expand its outdoor sporting goods. Chicago has a high per capital income and a high employment rate.

References