In of fit” statistic, because it measures how well

In an effort to determine
if the whether or not new sales software is affecting the performance of salespeople
in four regions in which the company operates, the Northeast, Southeast,
Central, and West regions, I have created breakdown of the available sales data
since software implementation using the Chi-Square statistics and hypothesis
testing methods. The sales data I will be using reflects salespeople, totaling
500, who were divided in half, with half of them being provided with the sales
software and half of them not over the period of three months.

Part of this study is to
determine possible null and alternative hypotheses for a nonparametric test on
this data using chi-square distribution. To better describe these types of
hypotheses I refer to Dr. Tom Pierce of Raddford University (2010) who defines
them as “The null hypothesis is that the researcher’s prediction is not true.
The alternative hypothesis is that the researcher’s predicted difference is
true. So, the two-sample t-test gives us a way to decide between a null
hypothesis and an alternative hypothesis.” This study will use the
nonparametric qualitive data category of region. Elaborating, nonparametric data
is used on qualitive or categorical data such and gender, color, or the aforementioned
category of region.

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The null hypothesis in
this study is that sales software does not make a difference in the performance
of salespeople in their duty to sell a certain number of products and therefore
that there is no statistical significance between the variable of having sales
software and an increase in sales. The alternative hypothesis in this study is
that there is a statistically significant relationship between the performance
of the sales people and whether or not they were provided with the new sales
software.

 

The chi-square test “is
intended to test how likely it is that an observed distribution is due to
chance. It is also called a “goodness of fit” statistic, because it
measures how well the observed distribution of data fits with the distribution
that is expected if the variables are independent.” (Dept. of Linguistics, Penn
State University, 2008) In this study I will use chi-square to analyze the
categorical data which has been provided.

 

Using the chi-square test
I have used the data to calculate the expected distribution. The estimated
value for each cell is the total for its row multiplied by the total for its
column, then divided by the total for the table: that is,
(RowTotal*ColTotal)/GridTotal (Dept. of Linguistics, Penn State University,
2008). The second table (below) now shows the distribution of the totals which
is based on the null hypothesis that the sales software will not have an impact
on the sales of salespeople in each region. In contrast you will see the first
table which reflects the actual data. The third table is the expected data. The
final table is the chi-square calculations.

 

 

 

Region

Software

No-Software

Totals

Actual Data

Northeast

165

100

265

Southeast

200

125

325

Central

175

125

300

West

180

130

310

Total

720

480

1200

Region

Software

No-Software

Totals

Null Hypothesis

Northeast

132.5

132.5

265

Southeast

162.5

162.5

325

Central

150

150

300

West

155

155

310

Total

600

600

1200

Region

Software

No-Software

Totals

Expected

Northeast

159.00

106.00

265.00

Southeast

195.00

130.00

325.00

Central

180.00

120.00

300.00

West

186.00

124.00

310.00

Total

720.00

480.00

1200.00

In order to complete the following table the cv and degrees of
freedom were calculated.

Observed

Expected

(O-E)

(O-E)2

(O-E)2/E

165

132.5

32.5

1056.25

7.97

200

162.5

37.5

1406.25

8.65

175

150

25

625

4.16

180

155

25

625

4.03

100

132.5

-32.5

1056.25

7.97

125

162.5

-37.5

1406.25

8.65

125

150

-25

625

4.16

130

155

-25

625

4.03

49.62

CV

7.814

( 3df and .05%

 

 

Based on the findings
here using the chi-square method, the null hypothesis must be rejected. The
observed chi-square of 49.62 is far higher than the 7.814 CV chi-square which
indicates that there is indeed a correlation between the amount of sales that a
salesperson makes and whether or not they are utilizing the new sales software
which also proves that we must accept the alternative hypothesis. As Stephanie
Glen (2013) of Statistics How To said, “A small chi-square value means that
there is very little relationship between your two variables. A larger value
means that there is a greater relationship between your two variables.”
Clearly, there is a strong relationship between our variable of use of sales
software and salesperson sales.