MAT 243 Project Two Summary Report Template
docx
keyboard_arrow_up
School
Southern New Hampshire University *
*We aren’t endorsed by this school
Course
243
Subject
Mathematics
Date
Jan 9, 2024
Type
docx
Pages
7
Uploaded by EarlSteel9150
MAT 243 Project Two Summary Report
Southern New Hampshire University
1.
Introduction: Problem Statement
This summary report will analyze a large historical data set to find data patterns. The data
sets are from Chicago Bulls from years 1996-1998 and from Boston Celtics from 2013-2015.
To find out the statistical significance of the claims about the performance of the Celtics,
several hypothesis tests will be conducted out. In order to complete the analysis for this
summary, I will use hypothesis tests to find the population mean, the population proportion,
and the difference between two population means.
Critical claims will be supported by data
in this analysis, and statistically significant findings will be obtained to help in the
improvement of the Celtics' performance in upcoming seasons.
2.
Introduction: Your Team and the Assigned Team
The team that I picked for this analysis is the Boston Celtics from the year 2013-2015.
And the team that was assigned to me for the comparative study is the Chicago Bulls from
the years 1996-1998.
Table 1. Information on the Teams
Name of Team
Years Picked
1. My Team
Chicago Bulls
1996-1998
2. Assigned
Boston Celtics
2013-2015
3.
Hypothesis Test for the Population Mean (I)
By assuming characteristics of one or more populations, hypothesis testing is used to test
claims about population mean claims. After making this assumption, the decision is made as to
whether the null hypothesis should be accepted or rejected.
The null Hypothesis is denoted by H
0
is a statement assumed to be true unless sufficient data
indicates otherwise.
The population parameter's function is to test the accuracy of the provided
experimental data, and the null hypothesis explains it. In short, depending on the viability of
the given population or sample, this hypothesis is either rejected or not rejected.
The
null
hypothesis (H
0
) stated that the average relative skill level of my team the Boston Celtics in the
year 2013-2015 is equal to 1340.
The alternative Hypothesis is denoted by H
a,
disputes the null hypothesis.
An alternative
hypothesis claims that the parameters for two populations are different or that the true value
of the population parameter is not the same as the hypothesized value.
The alternative
hypothesis (H
a
) states that the average relative skill level of my team the Boston Celtics in the
year 2013-2015 is greater than 1340.
The level of Significance is a value in which p-value is compared with to determine if the
null hypothesis is true or false. The level of significance for this hypothesis is 5% (
α = 0.05)
.
Table 2: Hypothesis Test for the Population Mean (I)
Statistic
Value
Test Statistic
28.05
P-value
0.0
The table shows that the P-value of 0.0 is less than the level of significance which 5%
(0.05), sufficient evidence exists to reject the null hypothesis (H
0
) that the average relative skill
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
level of my team the Boston Celtics in the year 2013-2015 is equal to 1340 in favor of the
alternative hypothesis (H
a
) that average relative skill level of my team in the year 2013-2015 is
greater than 1340.
Since the relative skill of my team in the years 2013-2015 is 1456.78 and is greater than
1340, my team did a good in the years 2013-2015.
4.
Hypothesis Test for the Population Mean (II)
The null hypothesis (H
0
) stated that the score of my team the Boston Celtics in the year 2013-
2015 is equal to 106 points. The alternative hypothesis (H
a
) states that the score of my team the
Boston Celtics in the year 2013-2015 is at an average of less than 106 points. The level of
significance is 1% (
α=0.01)
.
Table 3: Hypothesis Test for the Population Mean (II)
Statistic
Value
Test Statistic
324.46
P-value
0.0
The table shows that the P-value of 0.0 is less than the level of significance which 1% (0.01),
sufficient evidence exists to reject the null hypothesis (H
0
) that the score of my team the Boston
Celtics in the year 2013-2015 is equal to 106 points in favor of the alternative hypothesis (H
a
)
that the score of my team is at an average of less than 106 points.
This just serves to support the
team coach hypothesis that my team scored at an average of less than 106 points because my
team points in the year of 2013-2015 is 98.05 points only.
5.
Hypothesis Test for the Population Proportion
In general, hypothesis testing is used to test claims about a population proportion is
calculated to determine whether the population proportion is the same as the hypothesized
proportion P
0.
For this hypothesis the null hypothesis (H
0:
P=P
0
) is the management claims that
the proportion of games that my team Boston Celtics wins when scoring 102 or equal points is
0.90 (H
0:
P=0.90). The alternative hypothesis is the management claims that the proportion of
games that my team Boston Celtics wins when scoring 102 or more points is 0.90 (H
a:
P>0.90).
The level of significance for this hypothesis is 5% (
α = 0.05).
Table 4: Hypothesis Test for the Population Proportion
Statistic
Value
Test Statistic
18.52
P-value
0.0
Since the p-value is 0.0 and is less than the significance value of 0.05 (5%), sufficient
evidence exists to reject the null hypothesis H
0
in favor of the alternative hypothesis H
a.
This
evidence shows that when the Celtics score 102 points or more, they win more than 90% (0.90)
of games.
6.
Hypothesis Test for the Difference Between Two Population Means
The hypothesis test for the difference between two population means is used when comparing
two sets of data to see if they are equal or not.
For this hypothesis the null hypothesis (H
0:
μ
1
=
μ
2
)
is that the skill level of my team the Boston Celtics in 2013-2015 is equal to the skill level of
the Bulls in 1996 to 1998. On the other hand, the alternative hypothesis is (H
a:
μ
1
≠ μ
2
) is that the
skill level of my team the Boston Celtics in 2013-2015 is not equal to the skill level of the Bulls
in 1996 to 1998
. The level of significance for this hypothesis is 1% (α = 0.01).
Table 5: Hypothesis Test for the Difference Between Two Population Means
Statistic
Value
Test Statistic
53.41
P-value
0.0
As the table shows, the p-value is 0.0 means that since the p- value is less than the
significance level (α
= 0.01) sufficient evidence to reject the null hypothesis in favor of the
alternative hypothesis that the
skill level of
Celtics in 2013-2015 is not equal to the skill level of
the Bulls in 1996-1998.
This test reveals that, in order for the Boston Celtics' skill level to equal the skill level of
the Chicago Bulls, management must work together with the team to improve the Celtics' skill
level.. Because the skill level of the Bull is 1739.8 while my team is 1456.78.
7.
Conclusion
The analyzed data's practical use may be seen in the average points scored by two teams
throughout a period of years, the number of games they won, the number of games they won
in which they scored 102 points or more, and finally, the mean relative skill level.
In conclusion, I received a p-value of 0.0 for each of these hypothesis tests, which is lower
than all significance levels for each test. The findings indicate that the Boston Celtics team from
2013 to 2015 had a good relative skill score of 1456.78, which is indicative of a team with
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
talented players and coaches. We can determine which team performed better using this data.
This information shows whether both teams and simply one exceeded expectations.
8.
Citations
ZyBooks
. (Fall 2023).
https://learn.zybooks.com/zybook/MAT-243-J1278-OL-TRAD-
UG.23EW1/chapter/1/section/2
(accessed September 28, 2023).