MAT 243 Project Two Summary Report Amber Smith

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Southern New Hampshire University *

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Feb 20, 2024

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MAT 243 Project Two Summary Report [Amber Smith] [amber.smith33@snhu.edu] Southern New Hampshire University

1. Introduction: Problem Statement This report will be an analysis of data to look for patterns in the dataset. The dataset is the Chicago Bulls from years 1996-1998 and the Pacers from years 2013-2015. Hypothesis tests will be done to regarding the Pacers performance data. By analyzing the tests the team can hope to improve the game performance of the Pacers. Methods to be used in this data analysis include hypothesis testing for finding the population mean and the proportion. I will also be finding the population mean difference between two teams. 2. Introduction: Your Team and the Assigned Team  I chose the Pacers with years 2013-2015. The assigned team for analysis comparison was Bulls for years 1996-1998. Table 1. Information on the Teams Name of Team Years Picked 1. Yours Pacers 2013-2015 2. Assigned Bulls 1996-1998 3. Hypothesis Test for the Population Mean (I) Suppose a relative skill level of 1340 represents a critically low skill level in the league. The management of your team has hypothesized that the average relative skill level of your team is greater than 1340. You tested this claim using a 5% level of significance. For this test, you assumed that the population standard deviation for relative skill level is unknown. Explain the steps you took to test this problem and interpret your results. a. Hypothesis testing is used for testing a population mean claim by making an assumption about one or more populations. Based off that you have to decide whether the null hypothesis is accepted or rejected. The null hypothesis is assumed to be true until the data proves it untrue. The null hypothesis is shown with H(0). The alternative hypothesis is H(a) and is an opposite contradicting statement than the null hypothesis. The level of significance is what the p value will be compared to for checking if the hypothesis is correct is not. Table 2: Hypothesis Test for the Population Mean (I) Statistic Value Test Statistic 30.97 P-value 0.00 b. This test states that the null hypothesis is the average relative skill of the Pacers from 2013-2015 is equal to 1340. The alternative hypothesis states that the average relative

skill of the Pacers from 2013-2015 is greater than 1340. The p value is 0 which is less than a 5% significance level. Because it is lower than the significance level then the null hypothesis will be rejected and the alternative hypothesis will be accepted. 4. Hypothesis Test for the Population Mean (II) Your team’s coach has hypothesized that average number of points scored by your team in the team’s years is less than 106 points. For this test, you assumed that the population standard deviation for points scored is unknown. You tested the claim using a 1% level of significance. Explain the steps you took to test this problem and interpret your results. The null hypothesis is that the Pacers during the years 2013-2015 on average score is equal to 106 points per game. The alternative hypothesis is they scored on average less than 106 points. The significance level is only 1% for this test. The p value is zero which is still less than the significance level of 1%. The null hypothesis should be rejected and the alternative accepted. That would mean the average score per game was less than 106 points. Table 3: Hypothesis Test for the Population Mean (II) Statistic Value Test Statistic -14.66 P-value 0.00 5. Hypothesis Test for the Population Proportion Suppose the management claims that the proportion of games that your team wins when scoring 102 or more points is 0.90. You tested this claim using a 5% level of significance. Explain the steps you took to test this problem and interpret your results. The null hypothesis will be P=P(0) meaning that the proportion of games won by the Pacers is 50%. The alternative hypothesis would be that the proportion of games won would be greater than 50%. The significance level is 5%. The p value is more than the significance level which means that the alternative hypothesis would be accepted which is winning more than 50% of games with points 102 or higher. Table 4: Hypothesis Test for the Population Proportion Statistic Value Test Statistic 0.00 P-value 1.0 6. Hypothesis Test for the Difference Between Two Population Means

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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. The null hypothesis shows the skill level for the Pacers 2013-2015 is equal to the Bulls 1996-1998. The alternative hypothesis states that the skill levels for the pacers and bulls are not equal. The significance level for this is 1%. The p value is 0 which means the skill levels for the two teams are not equal. Table 5: Hypothesis Test for the Difference Between Two Population Means Statistic Value Test Statistic 31.36 P-value 0.00 7. Conclusion In conclusion the experiments mostly had a p value of 0.0. That is lower than significance levels as well. The relative skill level for the Pacers is 1562.57 which is lower than the bulls which was 1739.8. That means the Pacers need to work harder and develop their team to play at a higher relative skill level. The pacers do win over 50% of games with score of 102 or higher. 8. Citations You were not required to use external resources for this report. If you did not use any resources, you should remove this entire section. However, if you did use any resources to help you with your interpretation, you must cite them. Use proper APA format for citations. Insert references here in the following format: Author's Last Name, First Initial. Middle Initial. (Year of Publication). Title of book: Subtitle of book, edition. Place of Publication: Publisher.

MAT 243 Project Two Summary Report Amber Smith

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