MAT 243 Project Two Summary Report Template (2)
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School
Southern New Hampshire University *
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Course
243
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Mathematics
Date
Feb 20, 2024
Type
docx
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6
Uploaded by ElderMandrill771
MAT 243 Project Two Summary Report
Courtney McDonald
Courtney.McDonald1@snhu.edu
Southern New Hampshire University
1.
Introduction: Problem Statement
I am using historical datasets for the Spurs to analyze performance patterns. I will also be
using the Bulls' historical data to compare with the Spurs sets and provide data evidence for possible feedback/conclusion. The timeline that will be used to group and filter the data gathered is for the game and points information for the Spurs games from the years 2013-2015, while the Bulls data is from the years 1996-1998. We conducted two hypothesis tests to find the population mean, or the average relative skill level of the Spurs in this case, and tested it against the hypothesis. We also conducted another test against the hypothesis for population proportion and the difference between the Bulls and
Spurs population means.
2.
Introduction: Your Team and the Assigned Team
Two teams were used to effectively perform the analysis and provide a comparison between datasets. The first team is mine, which is the Spurs and the range of years used was 2013-2015. The second team is an assigned team, the Bulls, and their range of years used was 1996-1998. It is displayed in the below table the teams used as well as the year ranges for each. Table 1. Information on the Teams
Name of Team
Years Picked
1. Yours
Spurs
2013 - 2015
2. Assigned
Bulls
1996- 1998
3.
Hypothesis Test for the Population Mean (I)
Hypothesis testing uses samples of specified data to evaluate a claim that a population mean has a certain value. In this project, I found the average relative skill level of the Spurs from the years 2013-2014, which was 1685.42. A null and alternative hypothesis was created with this information. The null hypothesis is that the population of the NBA mean is equal to 1685.42, while the alternative hypothesis states that the NBA population mean is not equal to 1685.42. This would be to prove the correlation between the averages of the Spurs and NBA skill level. The test statistic had a value of 168.11 and the p-value was 0.0. Since the p-value
is less than the alpha level of 0.05, this is statistically significant and different, therefore rejecting the null hypothesis. A second hypothesis test was then performed to evaluate the proportion of games that the team scored less than 106 points in the years 2013-2015. This was found to be 103.85, which is around the projected good score of 106. When evaluating to see if the NBA population
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proportions match the Spurs, the null hypothesis would be that the NBA population proportion would be equal to 103.85, and the alternative hypothesis would be that the population proportion for the NBA would not be equal to 103.85. The z-test statistic was -3.02 and the p-value was 0.0028. Since the p-value is less than the alpha level 0.01, it indicates that we should reject the null hypothesis. The last two steps we did were the comparison steps. We performed a hypothesis test to compare the two population means between my team and the team assigned. When comparing the two population means of the teams, there was a t-
statistic of 14.04 and a p-value of 0.0. Since the p-value 0.0 is less than 0.01, the null hypothesis would be rejected. This indicates that there was a statistically significant difference between the relative skills of the respective teams in the respective years.
Table 2: Hypothesis Test for the Population Mean (I)
Statistic
Value
Test Statistic
168.11
*Round off to 2 decimal places.
P-value
0.00
*Round off to 4 decimal places.
4.
Hypothesis Test for the Population Mean (II)
Table 3: Hypothesis Test for the Population Mean (II)
Statistic
Value
Test Statistic
-3.02
*Round off to 2 decimal places.
P-value
0.0028
*Round off to 4 decimal places.
5.
Hypothesis Test for the Population Proportion
Table 4: Hypothesis Test for the Population Proportion
Statistic
Value
Test Statistic
-0.55
*Round off to 2 decimal places.
P-value
0.58
*Round off to 4 decimal places.
6.
Hypothesis Test for the Difference Between Two Population Means
Table 5: Hypothesis Test for the Difference Between Two Population Means
Statistic
Value
Test Statistic
14.04
*Round off to 2 decimal places.
P-value
0.0
*Round off to 4 decimal places.
7.
Conclusion
Using data to correlate points, we can also conclude and come to a data-driven answer regarding a problem. With this project, we were tasked with using data sets from specific years for specific teams and also the NBA to evaluate the Spurs' performance which can be used to predict and aid performance for the next season. According to statistical data, the conclusion can be stated that the Spurs performed drastically differently than the Bulls and the average of the NBA. These changes were recorded at an 5% and 1% error margin, making the conclusion accurate.
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