MAT 243 Project Two Summary Report Template
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Southern New Hampshire University *
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Mathematics
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Feb 20, 2024
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MAT 243 Project Two Summary Report
Damien Holmes
Damien.holmes@snhu.edu
Southern New Hampshire University
1.
Introduction: Problem Statement
In this report, I have been tasked with analyzing a data set for two NBA teams, The Chicago Bulls from the years 1996 to 1998 and the Sixers from the year 2013 to 2015. With this data, I am attempting to gain some insight into the performance and skill levels of these two teams during these periods. To conduct the
analysis, a few statistical methods such as the t-test for the population mean, z-test for population proportions, and the t-test for the difference between the two population means will be used. With these tools, we will have some help in concluding the two teams during these periods and improve the Sixers on-court performance. 2.
Introduction: Your Team and the Assigned Team
In this comparative study, I chose the Sixers to do my analysis, focusing on the team from the years 2013 to 2018. The team I was assigned for this study, the Bulls will be evaluated from the years 1996 to 1998. The table below shows my chosen team and time frame and my assigned team and time frame.
Table 1. Information on the Teams
Name of Team
Years Picked
1. Yours
Sixers
2013 – 2015
2. Assigned
Bulls
1996- 1998
3.
Hypothesis Test for the Population Mean (I)
Hypothesis testing is a statistical method used to make inferences about population parameters based on sample data.
The null hypothesis states that the average relative skill level of my team is less than or equal to 1340.
H0:µ≤1340
The alternative hypothesis states that the average relative skill level of my team is greater than 1340.
Ha: µ>1340
The level of significance is 0.05 or 5%
The test statistic is calculated to be 1.28 and the p-value is calculated to be 0.2004
The test statistic value represents the number of standard errors the sample mean is away from the hypothesized population mean under the null hypothesis.
The p-value is the probability of there being a test statistic as extreme as 1.28 if the null hypothesis were true.
Conclusion: Since the p-value(0.2004) is greater than the significance level(0.05) we won't reject the null hypothesis.
Table 2: Hypothesis Test for the Population Mean (I)
Statistic
Value
Test Statistic
1.28
.
P-value
0.2004
4.
Hypothesis Test for the Population Mean (II)
The null hypothesis is that the average points scored by my team is greater than 106.
H0:µ≥106
The alternative is that the average points scored by my team is less than 106.
Ha: H0:µ<106
The level of significance = 0.01 or 1%
Conclusion: Since the p-value is less than the significance level, we will reject the null hypothesis. Table 3: Hypothesis Test for the Population Mean (II)
Statistic
Value
Test Statistic
-16.12
P-value
0.0000
5.
Hypothesis Test for the Population Proportion
The null hypothesis states that the proportion of games won when scoring 102 or higher is equal to 0.90 or 90%
H0: p=0.90
The alternative hypothesis states the proportion of games won when scoring 102 or higher is not equal to 0.90 or 90%
Ha: p≠0.90
The level of significance is equal to 0.05 or 5%
Conclusion: Since the p-value (0.0) is less than the given significance level(0.05), we reject the null hypothesis.
Table 4: Hypothesis Test for the Population Proportion
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Statistic
Value
Test Statistic
-9.4
P-value
0.0000
6.
Hypothesis Test for the Difference Between Two Population Means
You were asked to compare your team’s skill level (from its years) with the assigned team’s skill level (from the assigned time frame). You tested the claim that the skill level of your team is the same as the skill level of the assigned team, using a 1% level of significance. See Step 6 in the Python script to address the following items:
In general, how is hypothesis testing used to test claims about the difference between two population means?
Summarize all important steps of the hypothesis test. This includes:
a.
Null Hypothesis (statistical notation and its description in words)
b.
Alternative Hypothesis (statistical notation and its description in words)
c.
Level of Significance d.
Report the Test Statistic and the P-value in a formatted table as shown below:
Table 5: Hypothesis Test for the Difference Between Two Population Means
Statistic
Value
Test Statistic
X.XX
*Round off to 2 decimal places.
P-value
X.XXXX
*Round off to 4 decimal places.
e.
Conclusion of the hypothesis test and its interpretation based on the P-value
What are the implications of your findings from this hypothesis test? What is its practical significance?
Answer the questions in a paragraph response. Remove all questions and this note (but not the table) before submitting! Do not include Python code in your report. 7.
Conclusion
Describe the results of your statistical analyses clearly, using proper descriptions of statistical terms and concepts.
What is the practical importance of the analyses that were performed?
Describe what these results mean for the scenario.
Answer the questions in a paragraph response. Remove all questions and this note before submitting!
Do not include Python code in your report. 8.
Citations
How Hypothesis Tests Work: Significance Levels (Alpha) and P values - Statistics By Jim
Section 5.4 - MAT 243: Applied Statistics I for Science, Technology, Engineering, and Math | zyBooks
(732) MATH 243 - Project Two - YouTube