Southern New Hampshire University Team Performance Summary

MAT 243 Project Two Summary Report[Full Name]
[SNHU Email]
Southern New Hampshire University
Notes:
• Replace the bracketed text on page one (the cover page) with your personal information.
• You will use your selected team for all three projects
1. Introduction: Problem Statement
Discuss the statement of the problem in terms of the statistical analyses that are being performed. In
your response, you should address the following questions:
•
•
•
What is the problem you are going to solve?
What data set are you using?
What statistical methods will you be using to do the analysis for this project?
Answer the questions in a paragraph response. Remove all questions and this note before
submitting! Do not include Python code in your report.
2. Introduction: Your Team and the Assigned Team
In the Python script, you picked the same team and years that you picked for Project One. The assigned
team and its range of years will be the same as in Project One as well.
See Steps 1 and 2 in the Python script to address the following items in the table below:
•
•
What team did you pick and what years were picked to do the analysis?
What team and range of years were you assigned for the comparative study? (Hint: this is called
the assigned team in the Python script.) Present this information in a formatted table as shown
below.
Table 1. Information on the Teams
1. Yours
2. Assigned
Name of Team
Team (e.g. Knicks)
Team (e.g. Bulls)
Years Picked
XXXX-YYYY (e.g. 2013 – 2015)
XXXX-YYYY (e.g. 1996- 1998)
Answer the questions in a paragraph response. Remove all questions and this note (but not the
table) before submitting! Do not include Python code in your report.
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.
See Step 3 in the Python script to address the following items:
•
•
In general, how is hypothesis testing used to test claims about a population mean?
Summarize all important steps of the hypothesis test. This includes:
a. Null Hypothesis (statistical notation and its description in words)
b. Alternative Hypothesis (statistical notation and its description in words)
c. Level of Significance
d. Report the Test Statistic and the P-value in a formatted table as shown below:
Table 2: Hypothesis Test for the Population Mean (I)
Statistic
Test Statistic
P-value
•
Value
X.XX
*Round off to 2 decimal places.
X.XXXX
*Round off to 4 decimal places.
e. Conclusion of the hypothesis test and its interpretation based on the P-value
What are the implications of your findings from this hypothesis test? What is its practical
significance?
Answer the questions in a paragraph response. Remove all questions and this note (but not the
table) before submitting! Do not include Python code in your report.
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.
See Step 4 in the Python script to address the following items:
•
Summarize all important steps of the hypothesis test. This includes:
a. Null Hypothesis (statistical notation and its description in words)
b. Alternative Hypothesis (statistical notation and its description in words)
c. Level of Significance
d. Report the Test Statistic and the P-value in a formatted table as shown below:
Table 3: Hypothesis Test for the Population Mean (II)
Statistic
Test Statistic
P-value
f.
Value
X.XX
*Round off to 2 decimal places.
X.XXXX
*Round off to 4 decimal places.
Conclusion of the hypothesis test and its interpretation based on the P-value
•
What are the implications of your findings from this hypothesis test? What is its practical
significance?
Answer the questions in a paragraph response. Remove all questions and this note (but not the
table) before submitting! Do not include Python code in your report.
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.
See Step 5 in the Python script to address the following items:
•
•
In general, how is hypothesis testing used to test claims about a population proportion?
Summarize all important steps of the hypothesis test. This includes:
a. Null Hypothesis (statistical notation and its description in words)
b. Alternative Hypothesis (statistical notation and its description in words)
c. Level of Significance
d. Report the Test Statistic and the P-value in a formatted table as shown below:
Table 4: Hypothesis Test for the Population Proportion
Statistic
Test Statistic
P-value
•
Value
X.XX
*Round off to 2 decimal places.
X.XXXX
*Round off to 4 decimal places.
g. Conclusion of the hypothesis test and its interpretation based on the P-value
What are the implications of your findings from this hypothesis test? What is its practical
significance?
Answer the questions in a paragraph response. Remove all questions and this note (but not the
table) before submitting! Do not include Python code in your report.
6. Hypothesis Test for the Difference Between Two Population Means
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.
See Step 6 in the Python script to address the following items:
•
•
In general, how is hypothesis testing used to test claims about the difference between two
population means?
Summarize all important steps of the hypothesis test. This includes:
a.
b.
c.
d.
Null Hypothesis (statistical notation and its description in words)
Alternative Hypothesis (statistical notation and its description in words)
Level of Significance
Report the Test Statistic and the P-value in a formatted table as shown below:
Table 5: Hypothesis Test for the Difference Between Two Population Means
Statistic
Test Statistic
P-value
•
Value
X.XX
*Round off to 2 decimal places.
X.XXXX
*Round off to 4 decimal places.
e. Conclusion of the hypothesis test and its interpretation based on the P-value
What are the implications of your findings from this hypothesis test? What is its practical
significance?
Answer the questions in a paragraph response. Remove all questions and this note (but not the
table) before submitting! Do not include Python code in your report.
7. Conclusion
Describe the results of your statistical analyses clearly, using proper descriptions of statistical terms and
concepts.
•
•
What is the practical importance of the analyses that were performed?
Describe what these results mean for the scenario.
Answer the questions in a paragraph response. Remove all questions and this note before
submitting! Do not include Python code in your report.
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.
Project Two: Hypothesis Testing¶
This notebook contains the step-by-step directions for Project Two. It is very important to run
through the steps in order. Some steps depend on the outputs of earlier steps. Once you have
completed the steps in this notebook, be sure to write your summary report.
You are a data analyst for a basketball team and have access to a large set of historical data that
you can use to analyze performance patterns. The coach of the team and your management have
requested that you perform several hypothesis tests to statistically validate claims about your
team’s performance. This analysis will provide evidence for these claims and help make key
decisions to improve the performance of the team. You will use the Python programming
language to perform the statistical analyses and then prepare a report of your findings for the
team’s management. Since the managers are not data analysts, you will need to interpret your
findings and describe their practical implications.
There are four important variables in the data set that you will study in Project Two.
Variable What does it represent?
pts
Points scored by the team in a game
elo_n
A measure of relative skill level of the team in the league
year_id Year when the team played the games
fran_id Name of the NBA team
The ELO rating, represented by the variable elo_n, is used as a measure of the relative skill of a
team. This measure is inferred based on the final score of a game, the game location, and the
outcome of the game relative to the probability of that outcome. The higher the number, the
higher the relative skill of a team.
In addition to studying data on your own team, your management has also assigned you a second
team so that you can compare its performance with your own team’s.
Team
Your Team
Assigned
Team
What does it represent
This is the team that has hired you as an analyst. This is the team that you will
pick below. See Step 2.
This is the team that the management has assigned to you to compare against your
team. See Step 1.
Reminder: It may be beneficial to review the summary report template for Project Two prior to
starting this Python script. That will give you an idea of the questions you will need to answer
with the outputs of this script.
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Step 1: Data Preparation & the Assigned Team¶
This step uploads the data set from a CSV file. It also selects the Assigned Team for this analysis.
Do not make any changes to the code block below.
1. The Assigned Team is Chicago Bulls from the years 1996 – 1998
Click the block of code below and hit the Run button above.
In [1]:
import numpy as np
import pandas as pd
import scipy.stats as st
import matplotlib.pyplot as plt
from IPython.display import display, HTML
nba_orig_df = pd.read_csv(‘nbaallelo.csv’)
nba_orig_df = nba_orig_df[(nba_orig_df[‘lg_id’]==’NBA’) &
(nba_orig_df[‘is_playoffs’]==0)]
columns_to_keep =
[‘game_id’,’year_id’,’fran_id’,’pts’,’opp_pts’,’elo_n’,’opp_elo_n’,
‘game_location’, ‘game_result’]
nba_orig_df = nba_orig_df[columns_to_keep]
# The dataframe for the assigned team is called assigned_team_df.
# The assigned team is the Bulls from 1996-1998.
assigned_years_league_df = nba_orig_df[(nba_orig_df[‘year_id’].between(1996,
1998))]
assigned_team_df =
assigned_years_league_df[(assigned_years_league_df[‘fran_id’]==’Bulls’)]
assigned_team_df = assigned_team_df.reset_index(drop=True)
display(HTML(assigned_team_df.head().to_html()))
print(“printed only the first five observations…”)
print(“Number of rows in the dataset =”, len(assigned_team_df))
game_id
year_id fran_id pts opp_pts elo_n opp_elo_n game_location game_result
0 199511030CHI 1996
Bulls 105 91
1598.2924 1531.7449 H
W
1 199511040CHI 1996
Bulls 107 85
1604.3940 1458.6415 H
W
2 199511070CHI 1996
Bulls 117 108
1605.7983 1310.9349 H
W
3 199511090CLE 1996
Bulls 106 88
1618.8701 1452.8268 A
W
4 199511110CHI 1996
Bulls 110 106
1621.1591 1490.2861 H
W
printed only the first five observations…
Number of rows in the dataset = 246
Step 2: Pick Your Team¶
In this step, you will pick your team. The range of years that you will study for your team is
2013-2015. Make the following edits to the code block below:
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1. Replace ??TEAM?? with your choice of team from one of the following team names.
*Bucks, Bulls, Cavaliers, Celtics, Clippers, Grizzlies, Hawks, Heat, Jazz, Kings, Knicks,
Lakers, Magic, Mavericks, Nets, Nuggets, Pacers, Pelicans, Pistons, Raptors, Rockets,
Sixers, Spurs, Suns, Thunder, Timberwolves, Trailblazers, Warriors, Wizards*
Remember to enter the team name within single quotes. For example, if you picked the
Suns, then ??TEAM?? should be replaced with ‘Suns’.
After you are done with your edits, click the block of code below and hit the Run button above.
In [2]:
# Range of years: 2013-2015 (Note: The line below selects all teams within the
three-year period 2013-2015. This is not your team’s dataframe.
your_years_leagues_df = nba_orig_df[(nba_orig_df[‘year_id’].between(2013,
2015))]
# The dataframe for your team is called your_team_df.
# —- TODO: make your edits here —your_team_df =
your_years_leagues_df[(your_years_leagues_df[‘fran_id’]==’Sixers’)]
your_team_df = your_team_df.reset_index(drop=True)
display(HTML(your_team_df.head().to_html()))
print(“printed only the first five observations…”)
print(“Number of rows in the dataset =”, len(your_team_df))
game_id
year_id fran_id pts opp_pts elo_n opp_elo_n game_location game_result
0 201210310PHI 2013
Sixers 84 75
1545.1703 1568.7308 H
W
1 201211040NYK 2013
Sixers 84 100
1535.9276 1557.5126 A
L
2 201211050PHI 2013
Sixers 88 110
1513.0991 1580.3411 H
L
3 201211070NOH 2013
Sixers 77 62
1529.5587 1454.7487 A
W
4 201211090BOS 2013
Sixers 106 100
1541.7600 1562.3982 A
W
printed only the first five observations…
Number of rows in the dataset = 246
Step 3: Hypothesis Test for the Population Mean (I)¶
A relative skill level of 1420 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 in the years
2013-2015 is greater than 1420. Test this claim using a 5% level of significance. For this test,
assume that the population standard deviation for relative skill level is unknown. Make the
following edits to the code block below:
1. Replace ??DATAFRAME_YOUR_TEAM?? with the name of your team’s dataframe.
See Step 2 for the name of your team’s dataframe.
1. Replace ??RELATIVE_SKILL?? with the name of the variable for relative skill. See
the table included in the Project Two instructions above to pick the variable name.
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Enclose this variable in single quotes. For example, if the variable name is var2 then
replace ??RELATIVE_SKILL?? with ‘var2’.
1. Replace ??NULL_HYPOTHESIS_VALUE?? with the mean value of the relative skill
under the null hypothesis.
After you are done with your edits, click the block of code below and hit the Run button above.
In [3]:
import scipy.stats as st
# Mean relative skill level of your team
mean_elo_your_team = your_team_df[‘elo_n’].mean()
print(“Mean Relative Skill of your team in the years 2013 to 2015 =”,
round(mean_elo_your_team,2))
# Hypothesis Test
# —- TODO: make your edits here —test_statistic, p_value = st.ttest_1samp(your_team_df[‘elo_n’],
1420)
print(“Hypothesis Test for the Population Mean”)
print(“Test Statistic =”, round(test_statistic,2))
print(“P-value =”, round(p_value,4))
Mean Relative Skill of your team in the years 2013 to 2015 = 1347.75
Hypothesis Test for the Population Mean
Test Statistic = -11.97
P-value = 0.0
Step 4: Hypothesis Test for the Population Mean (II)¶
A team averaging 110 points is likely to do very well during the regular season. The coach of
your team has hypothesized that your team scored at an average of less than 110 points in the
years 2013-2015. Test this claim at a 1% level of significance. For this test, assume that the
population standard deviation for relative skill level is unknown.
You are to write this code block yourself.
Use Step 3 to help you write this code block. Here is some information that will help you write
this code block. Reach out to your instructor if you need help.
1.
2.
3.
4.
The dataframe for your team is called your_team_df.
The variable ‘pts’ represents the points scored by your team.
Calculate and print the mean points scored by your team during the years you picked.
Identify the mean score under the null hypothesis. You only have to identify this value
and do not have to print it. (Hint: this is given in the problem statement)
5. Assuming that the population standard deviation is unknown, use Python methods to
carry out the hypothesis test.
6. Calculate and print the test statistic rounded to two decimal places.
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7. Calculate and print the P-value rounded to four decimal places.
Write your code in the code block section below. After you are done, click this block of code and
hit the Run button above. Reach out to your instructor if you need more help with this step.
In [8]:
from scipy.stats import ttest_1samp
import numpy as np
mean_pts = your_team_df[‘pts’].mean()
print(“Mean Points =”,mean_pts)
test_statistic, p_value = st.ttest_1samp(your_team_df[‘pts’], 110)
print(‘T Stat = %.2f, P Value = %.4f’ % (test_statistic, p_value))
if p_value < 0.01: print("Reject the null hypothesis") else: print("Accept the null hypothesis") Mean Points = 94.86585365853658 T Stat = -21.91, P Value = 0.0000 Reject the null hypothesis Step 5: Hypothesis Test for the Population Proportion¶ Suppose the management claims that the proportion of games that your team wins when scoring 80 or more points is 0.50. Test this claim using a 5% level of significance. Make the following edits to the code block below: 1. Replace ??COUNT_VAR?? with the variable name that represents the number of games won when your team scores over 80 points. (Hint: this variable is in the code block below). 1. Replace ??NOBS_VAR?? with the variable name that represents the total number of games when your team scores over 80 points. (Hint: this variable is in the code block below). 1. Replace ??NULL_HYPOTHESIS_VALUE?? with the proportion under the null hypothesis. After you are done with your edits, click the block of code below and hit the Run button above. In [18]: from statsmodels.stats.proportion import proportions_ztest your_team_gt_80_df = your_team_df[(your_team_df['pts'] > 80)]
# Number of games won when your team scores over 80 points
counts = (your_team_gt_80_df[‘game_result’] == ‘W’).sum()
# Total number of games when your team scores over 80 points
nobs = len(your_team_gt_80_df[‘game_result’])
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p = counts*1.0/nobs
print(“Proportion of games won by your team when scoring more than 80 points
in the years 2013 to 2015 =”, round(p,4))
# Hypothesis Test
# —- TODO: make your edits here —test_statistic, p_value = proportions_ztest(counts, nobs, 0.50)
print(“Hypothesis Test for the Population Proportion”)
print(“Test Statistic =”, round(test_statistic,2))
print(“P-value =”, round(p_value,4))
Proportion of games won by your team when scoring more than 80 points in the
years 2013 to 2015 = 0.3053
Hypothesis Test for the Population Proportion
Test Statistic = -6.36
P-value = 0.0
Step 6: Hypothesis Test for the Difference Between Two
Population Means¶
The management of your team wants to compare the team with the assigned team (the Bulls in
1996-1998). They claim that the skill level of your team in 2013-2015 is the same as the skill
level of the Bulls in 1996 to 1998. In other words, the mean relative skill level of your team in
2013 to 2015 is the same as the mean relative skill level of the Bulls in 1996-1998. Test this
claim using a 1% level of significance. Assume that the population standard deviation is
unknown. Make the following edits to the code block below:
1. Replace ??DATAFRAME_ASSIGNED_TEAM?? with the name of assigned team’s
dataframe. See Step 1 for the name of assigned team’s dataframe.
1. Replace ??DATAFRAME_YOUR_TEAM?? with the name of your team’s dataframe.
See Step 2 for the name of your team’s dataframe.
1. Replace ??RELATIVE_SKILL?? with the name of the variable for relative skill. See
the table included in Project Two instructions above to pick the variable name. Enclose
this variable in single quotes. For example, if the variable name is var2 then replace ??
RELATIVE_SKILL?? with ‘var2’.
After you are done with your edits, click the block of code below and hit the Run button above.
In [20]:
import scipy.stats as st
mean_elo_n_project_team = assigned_team_df[‘elo_n’].mean()
print(“Mean Relative Skill of the assigned team in the years 1996 to 1998 =”,
round(mean_elo_n_project_team,2))
mean_elo_n_your_team = your_team_df[‘elo_n’].mean()
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print(“Mean Relative Skill of your team in the years 2013 to 2015
round(mean_elo_n_your_team,2))
=”,
# Hypothesis Test
# —- TODO: make your edits here —test_statistic, p_value = st.ttest_ind(assigned_team_df[‘elo_n’],
your_team_df[‘elo_n’])
print(“Hypothesis Test for the Difference Between Two Population Means”)
print(“Test Statistic =”, round(test_statistic,2))
print(“P-value =”, round(p_value,4))
Mean Relative Skill of the assigned team in the years 1996 to 1998 = 1739.8
Mean Relative Skill of your team in the years 2013 to 2015 = 1347.75
Hypothesis Test for the Difference Between Two Population Means
Test Statistic = 57.05
P-value = 0.0
End of Project Two¶
Download the HTML output and submit it with your summary report for Project Two. The
HTML output can be downloaded by clicking File, then Download as, then HTML. Do not
include the Python code within your summary report.
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