MAT 243 Project Two Summary Report Template
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School
Southern New Hampshire University *
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Course
243
Subject
Mathematics
Date
Jan 9, 2024
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docx
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MAT 243 Project Two Summary Report
Kaelyn Murphy
Kaelyn.Murphy@snhu.edu
Southern New Hampshire University
1.
Introduction: Problem Statement
As the data analyst for the Dallas Mavericks, I have been tasked by my management team
and the coach to prepare a report which will assist in finding areas where the team can improve
its performance. The analysis will provide evidence to validate critical claims and get statistically
valid findings that will help make key decisions to make the team better in upcoming seasons.
The data set being analyzed and used to find patterns is a large set of historical data. I will be
using the Python programming language to perform statistical analysis. The statistical method
being used is hypothesis testing to find the statistical significance of the claims made about the
Dallas Mavericks.
2.
Introduction: Your Team and the Assigned Team
I chose the Dallas Mavericks and was assigned the years of 2013-2015 to do the analysis.
The assigned team was the Chicago Bulls and the years assigned were 1996-1998.
Table 1. Information on the Teams
Name of Team
Years Picked
1. Yours
Dallas Mavericks
2013-2015
2. Assigned
Chicago Bulls
1996-1998
3.
Hypothesis Test for the Population Mean (I)
In general, hypothesis testing evaluates two statements (the null hypothesis and the
alternative hypothesis) about a population to determine which statement is supported by the
sample data. The null hypothesis
(H
0
) is about the population mean equaling a specific value
whereas the alternative hypothesis
(H
α
) reflects our claim. Hypothesis testing then compares the
significance level (α) to the P-Value to help us determine whether to accept or reject the null
hypothesis.
For the hypothesis test, we are told the null hypothesis states that the relative skill level
for the Dallas Mavericks between the years of 2013-2015 is 1340. This would give a null
hypothesis of
H
0
: µ = 1340 (where µ is the population mean). The alternative hypothesis, which
is the believed assumption of the teams’ management that the relative skill level for the Dallas
Mavericks between the years of 2013-2015 is greater than 1340. This would give an alternative
hypothesis of H
α:
µ > 1340. The level of significance is α
= 0.05. The test statistic is 64.36 and
the P-value is 0.0000.
Table 2: Hypothesis Test for the Population Mean (I)
Statistic
Value
Test Statistic
64.36
P-value
0.0000
To determine if we will reject or fail to reject our null hypothesis, we compare the P-
value to the significance level. If the P-value is greater than the significance level, we fail to
reject the null hypothesis. If the P-value is less than the significance level, we reject the null
hypothesis in favor of the alternative hypothesis. Our P-value at 0.0000 is less than the
significance level at 0.05 which means our null hypothesis is rejected and the test is significant.
This tells us that the average relative skill for the Dallas Mavericks between the years of 2013-
2015 is greater than 1340.
4.
Hypothesis Test for the Population Mean (II)
For the hypothesis test, we are told the null hypothesis states that the average number of
points scored by the Dallas Mavericks between the years of 2013-2015 is 106. This would give a
null hypothesis of
H
0
: µ = 106 (where µ is the population mean). The alternative hypothesis,
which is the believed assumption of the teams’ management that the average number of points
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scored by the Dallas Mavericks between the years of 2013-2015 is less than 106. This would
give an alternative hypothesis of H
α:
µ < 106. The level of significance is α
= 0.01. The test
statistic is -3.02 and the P-value is 0.0028.
Table 3: Hypothesis Test for the Population Mean (II)
Statistic
Value
Test Statistic
-3.02
P-value
0.0028
To determine if we will reject or fail to reject our null hypothesis, we compare the P-
value to the significance level. If the P-value is greater than the significance level, we fail to
reject the null hypothesis. If the P-value is less than the significance level, we reject the null
hypothesis in favor of the alternative hypothesis. Our P-value at 0.0028 is less than the
significance level at 0.01 which means our null hypothesis is rejected and the test is significant.
This tells us that the average points scored by the Dallas Mavericks between the years of 2013-
2015 is less than 106.
5.
Hypothesis Test for the Population Proportion
In general, hypothesis testing evaluates two statements (the null hypothesis and the
alternative hypothesis) about a population to determine which statement is supported by the
sample data. The null hypothesis
(H
0
) is the hypothesis that the proportion equals
P
o
whereas the
alternative hypothesis
(H
α
) reflects our claim about the population proportion. Hypothesis
testing then compares the significance level (α) to the P-Value to help us determine whether to
accept or reject the null hypothesis.
For the hypothesis test, we are told the null hypothesis (
H
0
: P = P
0
) states that the proportion
of games that the Dallas Mavericks win when they score 102 or more points is equal to 0.90.
This would give a null hypothesis of
H
0
: P = 0.90. The alternative hypothesis (H
α:
P
≠
P
0)
,
which is the believed assumption of the teams’ management that the proportion of games that the
Dallas Mavericks win when they score 102 or more points is greater than 0.90. This would give
an alternative hypothesis of H
α:
P > 0.90. The level of significance is α
= 0.05. The test statistic
is -6.02 and the P-value is 0.0000.
Table 4: Hypothesis Test for the Population Proportion
Statistic
Value
Test Statistic
-6.02
P-value
0.0000
To determine if we will reject or fail to reject our null hypothesis, we compare the P-
value to the significance level. If the P-value is greater than the significance level, we fail to
reject the null hypothesis. If the P-value is less than the significance level, we reject the null
hypothesis in favor of the alternative hypothesis. Our P-value at 0.0000 is less than the
significance level at 0.05 which means our null hypothesis is rejected and the test is significant.
This tells us that the alternative hypothesis that the proportion of games where the Dallas
Mavericks win when by a score of 102 or more points is not equal to 0.90 is accepted.
6.
Hypothesis Test for the Difference Between Two Population Means
Hypothesis testing is used to assess claims about the difference between two populations
means are evaluated using the same significance level and P-value procedures used in single
populations. The null hypothesis tells us that the 2013-2015 Dallas Mavericks skill level is equal
to the 1996-1998 Chicago Bulls skill level. The null hypothesis is then written as
H
0
: µ
1
= µ
2
.
The alternative hypothesis tells us that the 2013-2015 Dallas Mavericks skill level is not equal to
the 1996-1998 Chicago Bulls skill level. The alternative hypothesis is then written as
H
α
:
µ
1
≠
µ
2.
The level of significance is α
= 0.01. The test statistic is 40.55 and the P-value is 0.0000.
Table 5: Hypothesis Test for the Difference Between Two Population Means
Statistic
Value
Test Statistic
40.55
P-value
0.0000
The P-value is at 0.0000 is less than the level of significance at 0.01, which tells us we
can reject the null hypothesis and accept the alternative hypothesis. This tells us that the 2013-
2015 Dallas Mavericks skill level is not equal to the 1996-1998 Chicago Bulls Skill level.
7.
Conclusion
The importance of the analyses performed is that it helps us to see how the Mavericks compare
to other teams in the league by looking at historical data to make hypothesis. The analyses
highlight areas of improvements which allow management to make informed decisions on how
to improve overall performance for future seasons. The alternative hypothesis by management
that the Mavericks relative skill is greater than 1340 was accepted and by performing the Python
program calculations, we were able to see that the mean relative skill was 1551.46. The
alternative hypothesis by the management team that the Dallas Mavericks scored less than 106
points in the years 2013-2015 was accepted and by performing the Python program calculations,
we were able to see the mean points scored by the Mavericks in the years 2013-2015 was 103.73.
We know that to perform well during the regular season, we need to be closer to 106 points. The
management team then claimed that Dallas Mavericks skill level from 2013-2015 was the same
as the skill level of the Chicago Bulls from 1996-1998 which was rejected and seen by
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performing the Python program calculations. The Dallas Mavericks mean relative skill level
from 2013-2015 was 1551.46 whereas the mean relative skill level from 1996-1998 for the
Chicago Bulls was 1739.8.