MAT 243 Project Two Summary Report PDF

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MAT 243 Project Two Summary Report Ciara Rogers [email protected] Southern New Hampshire University

1. Introduction: Problem Statement

The problem that I am trying to solve is the historical data set to find data patterns. The data set are NBA official Chicago Bulls from 1996-1998 and the Miami Heat 2013-2015. This analysis will help team managers of the Miami Heat to improve their performance. 2. Introduction: Your Team and the Assigned Team

Table 1. Information on the Teams

1. Yours 2. Assigned

Name of Team Team Heat Team Bulls

Years Picked 2013 - 2015 1996- 1998

The team that I chose is MIami Heat and the years I picked were 2013-2015. The comparative study of the team that was assigned is the Chicago Bulls and the years are 1996-1998.

3. Hypothesis Test for the Population Mean (I)

The hypothesis testing used to test claims about a population mean claims by making assumptions about the parameter of one or more populations and then deciding whether the null hypothesis should be accepted or rejected. The Null Hypothesis is (H0) is a statement assumed to be true until enough data is proved otherwise. The alternative hypothesis (Hα) is a statement that contradicts the null hypothesis. The level of significance (α) is a value which the p-value and you determine the null is true or false.

Table 2: Hypothesis Test for the Population Mean (I) Statistic

Value

Test Statistic P-value

30.99 0.00

In this hypothesis test, it states the skill level of the Miami Heat from 2013-2015 is equal to 1420 (H0:µ= 1420). Because the management believes that the performance of the team skill is above 1420. The alternative hypothesis states that the relative skill of the team is greater than 1420 (Hα:µ > 1420). The p-value is 0.0 is less than the level of significance of 5% or 0.05, the null hypothesis would be rejected in favor of the alternative hypothesis. In other words, the other relative skill of the Miami Heat from 2013-2015 is higher than 1420. This will show the manager that their team is right on track with the player's skill set.

4. Hypothesis Test for the Population Mean (II)

The null hypothesis for this test will state the average number of points scored by Miami Heat. The Miami Heat in the years 2013-2015 is equal to 110 points (H0: µ = 110). The alternative hypothesis for this test states that the average points scored by the team in 2013-2015 is less than 110. The test was run using a level of significance of 10% or (α = 0.1)

Table 3: Hypothesis Test for the Population Mean (II) Statistic Test Statistic P-value

Value -14.42 0.0

Because the p-value of 0.0 is less than the level of significance of 10% or 0.1, the null hypothesis would be rejected in favor of the alternative hypothesis. In other words, the average points

scored by Miami Heat in 2013-2015 is less than 110 points. This would show the coach that he needs to work on the team performance when scoring points.

5. Hypothesis Test for the Population Proportion

Population proportion is generally used to determine if the population proportions (P) is similar to the hypothesized proportion (P0). In this case, the null hypothesis (H0:P=P0) states the proportion of the games that the Miami Heat played their wins 50% or 0.50 (H0:P= 0.50). The alternative hypothesis (Hα) states the proportion of the games the Miami Heat wins is greater than 50% or (0.50). The level of significance (a) is 5% (a=.05).

Table 4: Hypothesis Test for the Population Proportion Statistic Test Statistic P-value

Value -2575.25 0.0

Since the p-value of 0.0 is less than the signaficance level of 0.05, enough evidence exists to support the claim that Miami Heat wins when scoring 80 or more is greater than 50%.

6. Hypothesis Test for the Difference Between Two Population Means

Hypothesis testing the difference between two population means is used to test the difference between two sets of data to determine if the two sets are equal or not. The null hypothesis states the skill level of the Miami Heat during 2013-2015 is equal to the skill level of the Chicago Bulls

during 1996-1998. The alternative hypothesis will state that the level of the Miami Heat during 2013-2015 is not equal to the skill level of the Chicago Bulls during the 1996-1998. The level of significance (a) is 1% (a = 0.1)

Table 5: Hypothesis Test for the Difference Between Two Population Means Statistic Test Statistic P-value

Value 17.07 0.0

Based on the p-value of 0.0, there is sufficient evidence that the skill level of the Miami Heat is not equal to the skill level of the Chicago Bulls. This identifies the management needs to work on the team skill level and increase their skills as well.

7. Conclusion

In conclusion, in all four of these hypotheses, I had the p-value of 0.0. This is the lower level of significance in each test. Based on this I was able to determine whether the null hypothesis was rejected or accepted. This allowed me to decide where my team Miami Heat during 2013-2015 years needed to work on their skills or scoring and how they compare to the Chicago Bulls from 1996-1998....