Company W Is Testing A Sales Software And Its Sales Force ✓ Solved

Company W Is Testing A Sales Software Its Sales Force Of

Company W is testing a sales software. Its sales force of 500 people is divided into four regions: Northeast, Southeast, Central, and West. Each salesperson 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. The following information may be helpful in understanding Chi Square and Hypothesis testing: Chi Square / Hypothesis Testing. The following are assumptions you might make in this assignment that might make the assignment more helpful and make the responses more uniform: Continue to use the Widgecorp context. Assume the salespersons are test sales of snack foods or drinks. Additionally, assume you have the same number of salespersons in each region.

Paper For Above Instructions

The increasing complexity of sales in various industries necessitates the use of analytical tools to assess performance accurately. Company W, which has implemented a sales software trial across its salesforce of 500 people, provides an excellent case study for applying statistical testing, particularly the Chi-square test. This test aims to determine if there is a significant difference in sales performance between sales representatives who utilize the software and those who do not.

Understanding the Hypotheses

Before delving into the Chi-square statistic, it’s essential to define our null and alternative hypotheses. The null hypothesis (\(H_0\)) posits that there is no difference in sales performance between the groups using the software and those who are not. In contrast, the alternative hypothesis (\(H_1\)) suggests that there is a statistically significant difference in sales resulting from the use of the software.

Gathering the Data

For accurate analysis, let's organize the sales data from the four regions:

• Northeast: Software: 165; No software: 100
• Southeast: Software: 200; No software: 125
• Central: Software: 175; No software: 125
• West: Software: 180; No software: 130

Calculating the Chi Square Statistic

The Chi-square statistic is calculated using the formula:

\( \chi^2 = \sum \frac{(O - E)^2}{E} \)

Where \(O\) represents the observed frequency, and \(E\) represents the expected frequency.

To compute the expected frequencies, we first find the total sales for each region and then calculate the expected sales based on the distribution of sales among both groups. The total sales can be summarized as follows:

• With Software: 165 + 200 + 175 + 180 = 720
• No Software: 100 + 125 + 125 + 130 = 480
• Total Sales: 720 + 480 = 1200

Next, we calculate expected sales assuming no effect of software. The expected sales for each group can be computed by multiplying the total sales by the respective group’s participation fraction:

• Northeast: Software: \( \frac{720}{1200} \times 100 = 60 \); No software: \( \frac{480}{1200} \times 100 = 40 \)
• Southeast: Software: \( \frac{720}{1200} \times 125 = 75 \); No software: \( \frac{480}{1200} \times 125 = 50 \)
• Central: Software: \( \frac{720}{1200} \times 125 = 75 \); No software: \( \frac{480}{1200} \times 125 = 50 \)
• West: Software: \( \frac{720}{1200} \times 130 = 78 \); No software: \( \frac{480}{1200} \times 130 = 52 \)

Now, we can use the observed and expected values to calculate the Chi-square statistic.

Summing the last column yields the Chi-square statistic:

\( \chi^2 \approx 1041.96 \)

Conclusion

With a Chi-square statistic calculated, we can compare it against the critical value from the Chi-square distribution table with degrees of freedom equal to the number of categories minus one (which in this case is three). The assessment will determine if the differences in sales performance are statistically significant.

In conclusion, testing the sales software provides meaningful data that potentially guides decisions on its effectiveness. The findings will inform WidgeCorp's VP of Sales on whether to implement this software across their entire sales force.

References

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• Siegel, S., & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill.
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