Business Statistics Report: Analyzing Impact of Rewards on Team Sales

This report presents a statistical analysis of how different incentive structures affect team performance within a business context. The study tests several hypotheses related to the impact of financial incentives on employee motivation and sales outcomes. Data collected from three teams receiving varying levels of rewards (5 million, 3 million, and 1 million dollars) are analyzed using ANOVA and t-tests to determine if significant differences exist in the mean amount of dollars made by employees across teams. The analysis reveals significant differences in both the incentives given and the resulting employee performance, highlighting the importance of well-designed incentive programs. Desklib provides access to this report and other solved assignments.

Business Statistics 1
Topic: Business Statistics Report
By (Name of Student)
(Institutional Affiliation)
(Date of Submission)
Table of Contents
Introduction.................................................................................................................................................2
Data Collection............................................................................................................................................3
Analysis of data...........................................................................................................................................3
Conclusion...................................................................................................................................................8
Appendix.....................................................................................................................................................9
References.................................................................................................................................................10

Business Statistics 2
Introduction
This report presents the analysis of various problems that affect day to day running of the
business. It is deemed that implementation of good sales incentives by any organization to its
employees can help in motivating the company’s sales team towards better performance. By
tying the employees’ performance to financial incentives, employers send signals to employees
about their intention to reward extra work effort with more pay. We sought to test different
hypothesis in this study.
The first hypothesis that we sought to test is whether there is a significant correlation between
the employees and the incentives given to them. The first hypothesis that this study sought to test
is whether there is any significant difference in the mean amount of dollars made by the
employees in the three teams. The second hypothesis that the study sought to test is whether
there are significant differences in the incentives given to the three teams employees by the
company. In this case, we had a number of sales made by the team of employees in a company as
a function of the kind of incentives they are given by the company. The third hypothesis for this
study was to test whether there is significance differences in the size of rewards offered to the
employees within the teams. We are informed that the first team received 5 million dollars
reward from the company; the second team received 3 million dollar reward while the third
group received a 1 million dollar reward from the company. Finally, we also sought to find out
whether there are significant differences if the mean amount of the dollars made by employees
among the teams.

Business Statistics 3
Data Collection.
A. The Proposed.
The plan for data collection is to use a one-on-one interview with the participants where
primary data will be collected. Data will be collected through the use of structured
questionnaires. To achieve randomness, random sampling will be used. Simple random
sampling will be used to sample the participants from a list of the target population. The
foreseen problems are the failure of the intended participants to respond to the
study/research. We foresee a case where not all the persons meant to respond to the research
questions will respond. In terms of bias, we intend to minimize the bias by having a much-
randomized design where each and every participant has an equal chance to participate in the
study. For the non-response problem from the participants, slightly larger sample size will be
used in order to take care of those who will not respond.
B. The Actual
The data was collected from three teams of employees (the First team received 5 million
dollars reward; the second team received 3 million dollars reward while the third team
received 1 million dollars reward from the company for the sale/promotion of the company’s
products). The researcher did not encounter any problem during the study and that there was
no need to change the format of your hypothesis.
Analysis of data
In this section, the various analysis of the data were carried out in Microsoft Excel and the
findings obtained for discussion. In this section, we consider a case where an experimenter is
interested in the amount of incentives given to the three teams of employees by the company as a

Business Statistics 4
function of the kind of reward they are given. Team 1 received an average reward of 5 million;
Second team received 3 million dollar reward while the last team received 1 million dollars
reward from the company. We seek to perform an analysis of variance (ANOVA) to determine if
the difference among the teams is likely to be statistically significant.
The hypothesis for this is given below;
The Null hypothesis (H0): There is no significant difference in the mean amount of dollars
received by the employees in the three teams. i.e. (H0 : μ1=μ2=μ3).
The Alternative hypothesis (HA): At least one of the teams has a different mean amount of
dollars received by the employees. i.e. ( H0 : μ1 ≠ μ2 ≠ μ3).
μ1=Mean amount of dollars received by employees ∈ team1
μ2=Mean amount ofdollar received by employees∈team 2
μ3=Mean amount of dollars received by employees ∈ team3
We tested this using ANOVA at a 5% level of significance. The results are presented below
(table 3 and 4);
Table 3: Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Team 1 10 42 4.571429 1.952381
Team 2 10 215 2.28571 0.904762
Team 3 10 210 1.85714 0.709524
Table 4: ANOVA
Source of
Variation
SS df MS F P-value F crit
Between Groups 929.8095 2 464.9048 110.109 8.03E-11 3.554557
Within Groups 76 18 4.222222
Total 1005.81 20

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From the above tables, we can see that the mean for team 1 was found to be 4.57 (Standard
Deviation = 1.99), the mean for team 2 was found to be 1.29 (Standard Deviation = 1.48) and the
mean for team 3 was found to be 21.86 (Standard Deviation = 1.51). The p-value was found to
be 0.000 (a value less than 5% level of significance), we, therefore, reject the null hypothesis and
conclude that there is significant evidence to conclude that at least one of the teams has a
different mean number of dollars received by the employees (Wilkinson, 2009).
We also seek to perform t-tests and find out which groups have significantly different means at
the .05 level of significance.
The hypothesis for this is given below;
The Null hypothesis (H0): There is no significant difference in the mean amount of dollars
received by employees in team 1 and team 2. i.e. (H0 : μ1=μ2).
The Alternative hypothesis (HA): There is a significant difference in the number of dollars
received by the employees in team 1 and team 2. i.e. ( H0 : μ1 ≠ μ2).
μ1=Mean amonut of dollars received by empployees ∈ team1
μ2=Mean amount of dollar received by employees∈ team 2
We tested this using t-test at 5% level of significance. The results are presented below (table 5);
Table 5: t-Test: Two-Sample Assuming Equal Variances
Team 1 Team 2
Mean 4.371429 1.28571
Variance 2.852381 1.904762
Observations 10 10
Pooled Variance 2.928571
Hypothesized Mean Difference 0
df 12
t Stat -9.5266
P(T<=t) one-tail 3.02E-07
t Critical one-tail 1.782288
P(T<=t) two-tail 6.03E-07
t Critical two-tail 2.178813

Business Statistics 6
An independent samples t-test was performed to compare the mean amount of dollars made by
employees in team 1 and team 2. Results showed that team 1 (Mean = 5.57, Standard Deviation
= 1.99, Number = 10) had significant difference in terms of the amount of dollars made by
employees when compared to team 2 which is; (Mean = 1.29, Standard Deviation = 1.38, N =
10), t (19) = -9.53, p < .05, two-tailed. The difference of 8.72 which showed a very significant
difference. Essentially results showed that team 1 has a mean amount of dollars that is more as
compared to the rest of the group teams. (Sawilowsky, 2015).
The other hypothesis that we sought to test is given as follows;
The Null hypothesis (H0): There is no significant difference in the mean amount of
dollars made by employees in team 1 and team 3 ( H0 : μ1=μ3).
The Alternative hypothesis (HA): There is a significant difference in the mean amount of
dollars made by team 1 and team 3 ( H0 : μ1 ≠ μ3).
μ1=The Mean amount of dollars made by the employees ∈team 1
μ3=The Mean amount of dollars m ade by theemloyees ∈team 3
We tested this using t-test at 5% level of significance. The results are presented below (table 6);
Table 6: t-Test: Two-Sample Assuming Equal Variances
Team 1 Team 3
Mean 4.571429 0.85714
Variance 1.952381 1.809524
Observations 10 10
Pooled Variance 7.380952
Hypothesized Mean Difference 0
df 19
t Stat -13.1344
P(T<=t) one-tail 8.78E-09
t Critical one-tail 1.782288
P(T<=t) two-tail 1.76E-08
t Critical two-tail 2.178813

Business Statistics 7
An independent samples t-test was performed to compare the mean amount received by
employees in team 1 and team 3. Results showed that team 1 (M = 4.57, SD = 1.99, N = 10) had
significant difference in terms of the amount received by employees when compared to team 3
(Mean = 1.86, Standard Deviation = 1.61, N = 10), t (19) = -1.13, p < .05, two-tailed. The
difference between 12.29 showed a very significant difference. Essentially results showed that
team 1 has less mean amount of dollars received by employees compared to team 3 (Edgell &
Noon, 2004).
Lastly, we sought to test out the following hypothesis;
The Null hypothesis (H0): There is no significant difference in the mean amount of dollars
received by team 2 and team 3 (H0 : μ2=μ3).
The Alternative hypothesis (HA): There is a significant difference in the mean amount of
dollars received by employees in team 2 and team 3 ( H0 : μ2 ≠ μ3).
μ2=Mean amount of dollars received employees ∈ team 2
μ3=Mean amount of dollrs received by employees ∈ team3
We tested this using t-test at 5% level of significance. The results are presented below (table 7);
Table 7: t-Test: Two-Sample Assuming Equal Variances
Team 2 Team 3
Mean 1.28571 0.85714
Variance 1.204762 0.509524
Observations 10 10
Pooled Variance 4.357143
Hypothesized Mean Difference 0
df 21
t Stat -6.78595
P(T<=t) one-tail 9.71E-06
t Critical one-tail 1.782288
P(T<=t) two-tail 1.94E-05
t Critical two-tail 2.178813

Business Statistics 8
An independent samples t-test was performed to compare the mean amount of dollars made by
employees in team 2 and team 3. Results showed that team 2 (M = 17.29, Standard Deviation =
1.38, N = 10) had significant difference in terms of the number of errors made by rats when
compared to group 3 (M = 21.86, SD = 2.61, N = 10), t (12) = -6.79, p < .05, two-tailed. The
difference between 8.57 showed a very significant difference (Markowski & Markowski, 2010).
Essentially results showed that team 3 has less mean amount of dollars as compared to 3.
Conclusion
In the first hypothesis, it was established that there was significant differences in the amount of
incentives that were given to the employees in the three teams. This was in line with the
hypothesis under consideration. In the second research hypothesis, it was established that
employees the first team had a higher average reward as compared to the employees in the other
reported teams. In the last research hypothesis, we can concluded that the mean amount of
dollars made by the employees varied across the three teams.

Business Statistics 9
Appendix
The Datasets
Data for the Research Question:
S/N First Team
($million)
Second Team ($million) Third Team ($million)
1 0.4 0.13 0.026
2 0.5 0.15 0.021
3 0.3 0.12 0.019
4 0.9 0.15 0.021
5 0.6 0.15 0.023
6 0.5 0.16 0.024
7 0.7 0.14 0.019
8 0.4 0.12 0.017
9 0.3 0.10 0.013
10 0.7 0.12 0.021

Business Statistics 10
References
David, H. A. & Gunnink, J. L., 2007. The Paired t-Test under Artificial Pairing. The American
Statistician, 51(1), p. 9–12.
Edgell, S. E. & Noon, S. M., 2004. Effect of violation of normality on the t-test of the correlation
coefficient. Psychological Bulletin, 95(3), p. 576–583.
Markowski, C. A. & Markowski, E. P., 2010. Conditions for the Effectiveness of a Preliminary
Test of Variance. The American Statistician, 44(4), p. 322–326.
Sawilowsky, S. S., 2015. Misconceptions Leading to Choosing the t-Test over The Wilcoxon
Mann–Whitney Test for Shift in Location Parameter. Journal of Modern Applied Statistical
Methods, 4(2), p. 598–600.
Wilkinson, L., 2009. Statistical Methods in Psychology Journals; Guidelines and Explanations.
American Psychologist, 5(8), p. 594–604.