Project Two Summary Report
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School
Southern New Hampshire University *
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Course
240
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Mathematics
Date
Jan 9, 2024
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docx
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Uploaded by ProfRabbitMaster904
MAT 243 Project Two Summary Report
Joseph Tangen
Joseph.Tangen@SNHU.eud
Southern New Hampshire University
1.
Introduction: Problem Statement
We are completed some hypothesis testing to validate the performance of the Warriors compared to other teams in the league in 2013-2015, and we’re comparing them to the Bulls in 1996-1998 where they won three championships in a row to see skill level relative to other teams in the league and that the Warriors score more than 106 points per game on average. The data set being used is hypothesis tests for mean and population proportion to find the requested information. The statistical method that I’ll be using for the analysis for this project is inferential statistics, which is where we draw conclusions from the data that we have. In this case we
have population mean and population proportion tests to pull information from and draw conclusions to the hypotheses provided by management and the coach. 2.
Introduction: Your Team and the Assigned Team
The team I chose was the Warriors, the years that were selected were 2013-2015. The assigned team is the Bulls and the years that were provided were 1996-1998. Table 1. Information on the Teams
Name of Team
Years Picked
1. Yours
Warriors
2013-2015
2. Assigned
Bulls
1996-1998
3.
Hypothesis Test for the Population Mean (I)
Hypothesis testing for population mean is used to determine if the population mean is the same as the hypothesized mean, assuming the standard deviation is known. If the standard deviation isn’t known, then we would use a t-test to compare observed sample mean to a hypothesized mean. is used to assess the plausibility of an outcome by using sample data. The analysis would
provide evidence about the plausibility of the hypothesis, and the hypothesis would be measuring and examining random sample of population being analyzed. There are two tests that can be completed when testing population mean. If σ population standard deviation is known then we use a Z test, if σ population standard deviation is unknown we would use a t test. We’ll have X: be the relative skill in the league, and µ be the average relative skill of the Warriors.
The null hypothesis is average relative skill level of the Warriors is over 1340 so it would look like H0: µ=1340. The alternative hypothesis is average relative skill of the Warriors
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is greater than 1340, which would look like Ha: µ>1340. The level of significance is 0.05. The test statistic is 46.95 and the P-value is 0.0. Statistic
Value
Test Statistic
46.95
P-value
0.00
The p-value < the level of significance we would reject the null hypothesis. There is enough evidence to support management’s hypothesis that the average relative skill of the Warriors is above 1340. 4.
Hypothesis Test for the Population Mean (II)
We’ll have X: be the number of points scored by the Warriors in 2013-2015, and µ is the average number of points scored by the Warriors in 2013-2015.
The null hypothesis is H0: Which is the average number of points scored by the Warriors in years
2013-2015 is 106 points, so it would look like H0: µ = 106. The alternative hypothesis is Ha: which is the average number of points scored by the Warriors in 2013-2015 is less than 106 points, so it would look like Ha: µ < 106. The level of significance is 0.01. The test statistic is 1.18 and the P-value is 0.2400. Table 3: Hypothesis Test for the Population Mean (II)
Statistic
Value
Test Statistic
1.18
P-value
0.2400
Since the p-value is less than the level of significance we would fail to reject the null hypothesis. There is not enough evidence to support the coach’s hypothesis that the average number of points
scored by the Warriors in 2013-2015 is less than 106 points. 5.
Hypothesis Test for the Population Proportion
Hypothesis testing for population proportion is used to determine if the proportion is equal to the hypothesized proportion. In this case we’re provided data saying that if the Warriors are scoring 102 points or more the chances of them winning are 90%. We’ll have p: be population proportion of games that the Warriors win when they score more than 102 points. The null hypothesis is H0: which is proportion of games that the Warriors win when scoring 102 or more points is 0.90, it would look like H0: p = 0.90. The alternative hypothesis is Ha: which is proportions of games that the Warriors when scoring more than 102 points, which would look like Ha: p ≠ 0.90. The level of significance is 0.05. The test statistic is -2.78 and the P-value is 0.0055. Table 4: Hypothesis Test for the Population Proportion
Statistic
Value
Test Statistic
-2.78
P-value
0.0055
Since the p-value is less than the level of significance we would reject the null hypothesis. There wouldn’t be enough evidence to support management’s claim that the proportion of games that the Warriors win are when they score more than 102 points.
6.
Hypothesis Test for the Difference Between Two Population Means
For hypothesis testing an analyst would test statistical sample data to provide evidence on
the plausibility of the null hypothesis. The statistical analyst tests a hypothesis by measuring and examining a random sample of the population being looked at. One of the two hypotheses will always be true. We’ll have X: be the Warriors skill level, Y: will be the Bulls skill level. µ1: will be Average skill level of the Warriors and µ2: will be average skill level of the Bulls. The null hypothesis is H0: the average skill level of the Warriors is the same skill level of the Bulls Ha: µ1 = µ2. The alternative hypothesis is HA: average skill level of the Warriors is
the same as the Bulls, Ha: µ1 ≠ µ2. The level of significance is 0.01. The test statistics is 20.18 and the p-value is 0.0.
Table 5: Hypothesis Test for the Difference Between Two Population Means
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Statistic
Value
Test Statistic
20.18
P-value
0.00
Since the p-value is less than the level of significance we would reject the null hypothesis. There is not enough evidence to support the claim that the skill level of the Warriors is the same as the Bulls. 7.
Conclusion
The practical importance of performing the analyses is to see how the Warriors compare to other teams in the league in terms of relative skill and how they compare to other teams that were extremely successful in the year ranges given. The Bulls won the championship in 1996-1998, so comparing the Warriors to the Bulls compares how the skill level, points earned, and games won helps to estimate how well the team should do as they play teams in the league while hopping to win the championship. Using hypothesis testing such as population mean to figure out the skill level helps see how the Warriors compare to other teams around the league in 2013-2015. The results mean that the Warriors average skill is higher than the hypothesis, so the team has
a higher chance of winning games due to the relative skill level across the league. It also shows that Warriors score more than 102 points a game on average and that there is not enough evidence to support that the Warriors and Bulls skill level are the same when compared.