Download qui-square distibution and the new sales software

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