Scenario
WidgeCorp became the market leader in snack foods after acquiring a rival company, Company W. Their management style and business decision-making differed. Employees at WidgeCorp collected relevant data and through statistical analysis used this information to draw conclusions and make appropriate recommendations. Company W tended to rely on the experience and judgment of its managers. For the time being, both companies are being managed separately, but within the next twelve months they will merge all management, processes, and accounting. You work for Company W and are a little nervous about this new way of working, but realize that you need to be able to present issues and recommendations with statistical verification to the WidgeCorp executives. You will also introduce and employ statistical analysis to the senior management of Company W's various departments such as Marketing, Sales, and Production. Part of your job will be to educate Company W as well.
Company W is testing a sales software. Its sales force of 500 people is divided into four regions: Northeast, Southeast, Central, and West. Each sales person is expected to sell the same amount of products. During the last 3 months, only half of the sales representatives in each region were given the software program to help them manage their contacts. The Northeast using the software sold 165 and the group with no software sold 100, The Southeast with software sold 200 and the group with no software sold 125. The Central groups with software sold 175 and the group with no software sold 125. The West group with software sold 180 and the group with no software sold 130. Using this data calculate the Chi Square statistic.
The VP of Sales at WidgeCorp, who is comfortable with statistics, wants to know the possible null and alternative hypotheses for a nonparametric test on this data using the chi-square distribution. A nonparametric test is used on data that are qualitative or categorical, such as gender, age group, region, and color. It is used when it does not make sense to look at the mean of such variables. (You can refer to the article for this phase for further information.)