MAT 243 Project Two Summary Report Josh Rose 11-24-23
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Feb 20, 2024
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MAT 243 Project Two Summary Report
Joshua Rose
Southern New Hampshire University
1.
Introduction: Problem Statement
The problem at hand involves conducting a series of statistical analyses to address various questions related to two basketball teams, The Suns and the Bulls. The primary focus of these analyses is to gain insights into the performance and skill levels of each team during a specific period. The data sets used include information on the relative skill levels, points scored, and game winning proportions of the two teams. To conduct the analyses, statistical methods such as t-test for population means, z-tests for population proportions, and t-tests for the difference between two population means are used.
2.
Introduction: Your Team and the Assigned Team
For this comparative study, I have chosen the Suns for analysis, focusing on the years 2013 to 2015. For the assigned team, the Chicago Bulls were selected, with the years ranging from 1996 to 1998. This was the team and time frame assigned for this study within the script.
Table 1. Information on the Teams
Name of Team
Years Picked
1. Yours
Suns
2013 - 2015
2. Assigned
Chicago 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. In the context of testing claims about a population mean, here are the steps to test whether the average relative skill level of my chosen team is greater than 1340-
A.
Null Hypothesis (H0): µ ≤ 1340
The null hypothesis states that the average relative skill level of my team is less than or equal to 1340.
B.
Alternative Hypothesis (Ha): µ > 1340
The alternative hypothesis states that the average relative skill level of my team is greater than 1340.
C.
Level of significance: α
= 0.05
This represents the significance level or the probability of making a Type 1 error (rejecting the null hypothesis when its true). In this case, it is set at 5%. To conduct the hypothesis test, I used a t-test for population mean, assuming that the population standard deviation is unknown. This t-
test calculates a test statistic and a corresponding p-value.
Table 2: Hypothesis Test for the Population Mean (I)
Statistic
Value
Test Statistic
36.97
P-value
0.0000
D.
Test statistic: the calculated test statistic is 36.97
This value represents the number of standard errors the sample mean is away from the hypothesized population mean under the null hypothesis.
P-value: the p-value is calculated to be 0.00
This p-value is the probability of observing a test statistic as extreme as 36.97 (or more extreme)
if the null hypothesis were true.
E.
Conclusion
: Since the p-value is less than the chosen significance level (α = 0.05), we reject the null hypothesis.
Interpretation
: There is strong statistical evidence to conclude that the average relative skill level of my team is greater than 1340
Implications and Practical Significance: The findings of this hypothesis test indicate that my team’s average relative skill level is significantly higher than the critical level of 1340. This has practical significance for the team’s management as it suggests that they can be confident in their hypothesis that the team’s skill level is above the critical threshold. Having this information
could be used to make informed decisions related to player recruitment, training and overall team strategies.
4.
Hypothesis Test for the Population Mean (II)
To test the coach’s hypothesis that the average number of points scored by my team is less than 106 points:
A.
Null Hypothesis (H0): µ ≥ 106
The null hypothesis states that the average number of points scored by my team is greater than or equal to 106 points.
B.
Alternative Hypothesis (Ha): µ < 106
The alternative hypothesis states that the average number of points scored by my team is less than 106 points.
C.
Level of Significance: α = 0.01
This represents the significance level or the probability of making a Type 1 error (rejecting the null hypothesis when it is true). In this case it is set at 1%. To conduct the hypothesis test, a t-test is used for population mean, assuming that the population standard deviation is unknown. This t-test calculates a test statistic and a corresponding p-value.
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This negative value indicates how many standard errors the sample mean is away from the hypothesized population mean under the null hypothesis.
P-value: The p-value is calculated to be 0.00. This p-value is the probability of observing a test statistic as extreme as -6.41 (or more extreme) if the null hypothesis were true.
Table 3: Hypothesis Test for the Population Mean (II)
Statistic
Value
Test Statistic
-6.41
P-value
0.0000
Conclusion
: Since the p-value (0.00) is less than the chosen significance level (
α = 0.01), we reject the null hypothesis.
Interpretation
: There is strong statistical evidence to conclude that the average number of points scored
by my team is less than 106 points.
Implications and Practical Significance:
The findings of this hypothesis test suggest that, based on the sample data, the average number of points scored by my team is significantly less than the coach’s hypothesized value of 106 points. This has practical significance for the team’s strategy and coaching decisions. 5.
Hypothesis Test for the Population Proportion
Hypothesis testing for claims about a population proportion involves determining whether a sample proportion is significantly different from a hypothesized population proportion. These are the steps I used
to test the managements claim:
A.
Null Hypothesis (H0): p =0.90
The null hypothesis states that the proportion of games won when scoring 102 points or more is equal to 0.90 (as claimed by management).
B.
Alternative Hypothesis (Ha): p ≠
0.90
The alternative hypothesis states that the proportion of games won when scoring 102 or more points
is not equal to 0.90
C.
Level of Significance: α = 0.05
This represents the significance level or the probability of making a Type 1 error (rejecting the null hypothesis when its true). In this case, it is set at 5%. To conduct the hypothesis test for population proportion, I used a z-test. This test calculates a test statistic (z) and a corresponding p-value.
Table 4: Hypothesis Test for the Population Proportion
Statistic
Value
Test Statistic
-6.86
P-value
0.0000
Conclusion
: Since the p-value (0.0000) is less than the chosen significance level (
α = 0.05), we reject the null hypothesis.
Interpretation
: There is strong statistical evidence to conclude that the proportion of games won when scoring 102 or more points is different from the claimed value of 0.90.
Implications and Practical Significance
: The findings of this hypothesis test suggest that the management’s claim that the team wins 90% of its games when scoring 102 or more points is not supported by the data. This has practical implications for the team’s management as it indicates that the
team’s performance may be different from their original goal. Further analysis and adjustments may be needed to improve the team’s winning percentage when scoring at or above this points threshold. 6.
Hypothesis Test for the Difference Between Two Population Means
Hypothesis testing for the difference between two population means is typically used to determine whether there is a significant difference in the means of two separate populations. In this case, I am comparing the skill level of my team with the assigned team’s skill level.
Steps taken:
A.
Null Hypothesis (H0): µ1 = µ2
The null hypothesis states that the skill level of my team (µ1) is equal to the skill level of the assigned team (µ2). In other words, there is no significant difference between the skill levels of the two teams.
B.
Alternative Hypothesis (Ha): µ1 ≠ µ2
The alternative hypothesis states that the skill level of my team (µ1) is not equal to the skill level of the assigned team (µ2). It suggests that there is a significant difference in skill levels between the two teams.
C.
Level of Significance: α = 0.01
This represents the significance level or the probability of making a Type 1 error (rejecting the null hypothesis when it is true). In this case, it is set at 1%. To conduct the hypothesis test for the difference between two population means, I used a t-test for independent samples. This test calculates test statistics and a corresponding p-value.
Table 5: Hypothesis Test for the Difference Between Two Population Means
Statistic
Value
Test Statistic
45.75
P-value
0.0000
Conclusion
: Since the p-value (0.0000) is less than the chosen significance level (α
= 0.01), we reject the null hypothesis.
Interpretation
: There is strong statistical evidence to conclude that the skill level of my team is significantly different from the assigned team’s skill level.
Implications and Practical Significance
: The findings of this hypothesis test suggest that there is a significant difference in skill levels between my team and the assigned team. This has practical significance as it may inform decisions related to team strategy, training, and performance improvements.
7.
Conclusion
In conducting the statistical analyses for this comparative study, several key findings have been shown that carry practical importance for the teams and management involved.
In the analysis of the relative skill level of my team, the Suns, for the years 2013 to 2015, it was found that the average skill level was significantly higher than the critical level of 1340. This finding is of practical importance as it implies that the team possessed a higher skill level during these years, potentially impacting player recruitment options, training strategies and an overall team-based performance.
Also, when examining the average number of points scored by my team, it was determined that the average was significantly less than the hypothesized value of 106 points. This result suggests that there may be room for improvement in the team’s offensive capabilities, which could inform coaching strategies and player developments. Finally, in comparing the skill levels of my team, the Suns, with the assigned team, the Bulls, during their respective time frames, it was found that there was a significant difference in skill levels. This finding has practical significance for both teams as it suggests that the teams may require different strategies and directions to improve the performance of each teams skill levels.
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