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PHASE 3: INDIVIDUAL PROJECT KENNETH C HOLMES MGMT600-1502A-01 PROFESSOR HENRIETTA OKORO APRIL 27, 2015 QUI-SQUARE DISTRIBUTION OF THE SALES SOFTWARE Introduction: I have been asked by the VP of Sales to determine if sales software will help the sales force manage their contacts. Half their sales force was issued the software, and half were not, and they are expecting 100 percent compliance on achieving sales goals. It is my job to establish an (H0) and (H1) hypothesis, then make a determination using the chi-square distribution whether the software helps the sales force manager their client list. Hypothesis definition and process: I will start from the beginning. Hypothesis testing is essential for establishing research and conclusion for scientific research and business analysis for making the most informed, and educated decision possible. A hypothesis is an assumption or opinion about a problem, the value of data for a population, event or experiment. There are five steps in hypothesis testing: Test the null (H0) and alternative (H1) hypotheses; select the significance level (known as the confidence level or CV); calculate the numerical quantities or parameters from the sample specified by the H0; calculate the probability value, the probability of getting a different value from the data in the H0; compare the probability value to the significance level to determine whether to accept or reject the H0; and lastly, accept or reject the H0 based on the significance of the outcome (Lane, N.D.). Chi-square distribution definition and components: Chi-square distribution (x2) is the sum of the squares of k independent random variables, that compares the H0 and H1 hypotheses based on the degrees of freedom (DF) and the critical value (CV), to determine which hypothesis (assumption) is accepted or rejected. It is a special case of gamma probability distribution, is widely used for hypothesis testing and confidence interval estimation, is used in the test for goodness of fit, and test the independence of qualitative data (David Eck, N.D.). The x2 indicates the chi-square distribution value based on the number of degrees of freedom. The degree of freedom (DF) is a positive whole number that indicates the lack of restriction in our calculations, or the number of values in a calculation that we can vary, and is determined by the chi-square sample size. For smaller degrees of freedom it is a skewed distribution, and for larger degrees of freedom the x2 approaches normality. The critical value (CV) is the factor used to compute the margin of error. The X2 goodness of fit test helps determine whether the observed frequency of patterns fits the expected frequency of patterns, and to determine if the results are due to chance. X2 tests are nonparametric, meaning the data is qualitative or categorical that describes or illustrates, is not based on numbers or measurements, and does not draw conclusions. Instead it is based on characteristics, attributes, properties, and qualities including: gender, race, marital status, education level, sexual orientation, etc. (Kaushik, 2011). Chi-square distribution uses both numerical and categorical random variables, and determines if the distributions of categorical and numerical values differ from each other. Chisquare distribution compares the totals of numerical and categorical data from multiple independent groups, and can only be tested on actual numbers (Viswanathan, N.D.). Possible null and alternative hypotheses: Problem: Will additional advertising improve sales? H0: Additional advertising will not improve sales. H1: Additional advertising will improve sales. Problem: Will adding a cold beverage line increase sales? H0: Adding a cold beverage line will not increase sales. H1: Adding a cold beverage line will increase sales. Problem: Will enhancing the snack food line increase sales? H0: Enhancing the snack food line will not increase sales. H1: Enhancing the snack food line will increase sales. Problem: Will the sales software help WidgeCorp obtain new clients? H0: The sales software will not help WidgeCorp obtain new clients. H1: The sales software will help WidgeCorp obtain new clients. The process of the chi-square distribution (Deshpande, 2011): 1) 2) 3) 4) 5) 6) 7) 8) 9) Determine the problem to be solved with hypothesis testing. Specify the null (H0) and alternative (H1) hypothesis based on the problem to be solved. Gather data for analysis. Compute the degrees of freedom (DF) based on the contingency table. DF = (quantity of rows – 1) * (quantity of columns – 1). Determine the critical value (CV) based on the DF and the confidence level. Identify the X’s (dependent variable) and Y’s (independent variable). Compute the margin summations: Calculate the totals from all the rows and columns and enter their totals on the margins (total of rows and columns). Complete the contingency table. The totals from the rows and columns should both be equal. Compute the observed chi-square value based on data from the contingency table. a) Observed chi-square value = ∑ of all cells. 10) Compare the observed chi-square to the CV of chi-square based on the DF and confidence level, and determine whether to accept or reject the H0. a) If the observed chi-square < CV, then variable are independent and you accept the H0. b) If the observed chi-square>CV, then the variables are dependent and you reject the H0, and accept the H1. Chi-square symbols: H0 = Null hypothesis H1 = Alternative hypothesis DF = Degrees of freedom CV = Critical value The chi-square software analysis test: The problem: The software company claims their sales software will help WidgeCorp’s sales force manage their contact list. (H0): The sales software will not help the sales force manage their contact list. (H1): The sales software will help the sales force manage their contact list. Gathered data: Sales force of 500 in four regions: Northeast, Southeast, Central, and West. Expected values (E): Northeast:125, Southeast:125, Central:125, and West:125. Observed values (O) made goals: Northeast:110, Southeast:95, Central:90, and West:75. Observed values (O) did not make goals: Northeast:15, Southeast:30, Central:35, West:50. Degrees of freedom (DF): 4 samples, 4 – 1 = 3DF, or (4 rows–1) * (2columns–1) = 3*1 = 3DF Critical value (CV): 3df and (x2) 0.05 or 95% = 7.815 CV Data analysis: CHART 1 CONTINGENCY TABLE Regions Made Goal Did not make goal North East 110 15 South East 95 30 Central 90 35 West 75 50 Total: 370 130 Total 125 125 125 125 500 Chart 1 based on chart from (Eck, N.D.) CHART 2 CHI-SQUARE CALCULATIONS Observed Expected 110 125 15 125 95 125 30 125 90 125 35 125 75 125 50 125 Chi-square = Chart 2 based on chart from (Eck, N.D.) Every two rows represents one region from chart 1. (O-E) (O-E) 2 (O-E) 2/E 2 -15 225 1.8 Calculate the x for each outcome, made -110 12100 96.8 goals and did not make goals for each -30 900 7.2 region from Chart 1. -95 9025 72.2 Calculated the combined total of all x2. -35 1225 9.8 -90 8100 64.8 Compared the results from Chart 2 of the 2 2 -50 2500 20 observed x (317.6) to the CV x (7.815). -75 5625 45 Determined H0 2 is greater than the CV x 317.6 2, rejected the H0 and accepted the H1. x Results: Reject H0 because 317.6 observed chi-square from chart 2 is greater than 7.815 CV chi-square, ((x2) = 0.05 or 95%, and a DF of 3). Thus we reject H0 that there is no correlation between the sales software and sales. Our data tells us there is a correlation between the sales software and sales, and that is all is states. Conclusion: Based on this analysis the sales software appears to help the sales force manage their contacts. I would recommend purchasing the software for every sales person, require they learn how to use and apply it to obtain their goals, and address the issues of why some sales people are making their goals, and why others are not making their goals. Bear in mind it only accounts for how many sales people made and did not make their sales goals, it does not account for how many were and were not issued the software. If I designed an analysis with all four parameters: four rows and four columns would result in (DF = 9); a 9 DF and a 95 percent confidence level would provide a CV of 16.919; the H0 would still be rejected and the H1 would still be accepted; and the result would be the same. In addition to this analysis, I would recommend the Sales Manager email every sales person a questionnaire regarding their sales levels. For those who were issued the software the following questions need to be answered: if you are making your goals, does the software help you manage your contacts and make your goals, and why?; and how well does our product mix fit your markets and why? If you have not made your goals: do you understand how to use and apply the software and why?; are you unable to manage the size of your client list and why?; and are there issues with the product mix regarding your markets and why? For those who were not issued the software the following questions need to be answered: if you are making your goals, what are you doing that helps you make your goals?; and does the product mix work for your markets and why? If you are not making your goals: are you unable to manage the size of your client list and why?; and are there issues with the product mix regarding your markets and why? REFERENCES David Eck, a. J. (N.D.). The Chi-Square Statistic. Retrieved from math.hws.edu/javamath/ryan/ChiSquare.html Deshpande, B. (2011, march 14). 5 simple steps to apply chi-square test for business analytics. Retrieved from www.simafore.com/blog/bid/54885/5-simple-steps-to-apply-chi-square... Kaushik, N. (2011, August 13). Difference Between Qualitative Data and Quantitative Data. Retrieved from www.differencebetween.net/..../qualitative-data-and -quantitative-data Lane, D. M. (N.D.). Steps in Hypothesis Testing. Retrieved from www.davidmlane.com/hyperstat/B35642.html Viswanathan, P. (N.D.). Glimpses into Application of Chi-Square Tests in Marketing. Retrieved from www.davidmlane.com/hyperstat/viswanathan/chi_square_marketing.html