Question

The management wants to you to calculate a 95% confidence interval for the average relative skill of all teams in 2013-2015. To construct a confidence interval, you will need the mean and standard error of the relative skill level in these years. The code block below calculates the mean and the standard deviation. Your edits will calculate the standard error and the confidence interval. Make the following edits to the code block below:Replace ??SD_VARIABLE?? with the variable name representing the standard deviation of relative skill of all teams from your years. (Hint: the standard deviation variable is in the code block below)Replace ??CL?? with the confidence level of the confidence interval.Replace ??MEAN_VARIABLE?? with the variable name representing the mean relative skill of all teams from your years. (Hint: the mean variable is in the code block below)Replace ??SE_VARIABLE?? with the variable name representing the standard error. (Hint: the standard error variable is in the code block below)The management also wants you to calculate the probability that a team in the league has a relative skill level less than that of the team that you picked. Assuming that the relative skill of teams is Normally distributed, Python methods for a Normal distribution can be used to answer this question. The code block below uses two of these Python methods. Your task is to identify the correct Python method and report the probability.print("Confidence Interval for Average Relative Skill in the years 2013 to 2015")print("------------------------------------------------------------------------------------------------------------")# Mean relative skill of all teams from the years 2013-2015mean = your_years_leagues_df['elo_n'].mean()# Standard deviation of the relative skill of all teams from the years 2013-2015stdev = your_years_leagues_df['elo_n'].std()n = len(your_years_leagues_df)#Confidence interval# ---- TODO: make your edits here ----stderr = ??SD_Variable?? (n ** 0.5)conf_int_95 = st.norm.interval(??CL??,??MEAN_VARIABLE??,??SE_VARIABLE??)print("95% confidence interval (unrounded) for Average Relative Skill (ELO) in the years 2013 to 2015 =", conf_int_95)print("95% confidence interval (rounded) for Average Relative Skill (ELO) in the years 2013 to 2015 = (", round(conf_int_95[0], 2),",", round(conf_int_95[1], 2),")")print("\n")print("Probability a team has Average Relative Skill LESS than the Average Relative Skill (ELO) of your team in the years 2013 to 2015")print("----------------------------------------------------------------------------------------------------------------------------------------------------------")mean_elo_your_team = your_team_df['elo_n'].mean()choice1 = st.norm.sf(mean_elo_your_team, mean, stdev)choice2 = st.norm.cdf(mean_elo_your_team, mean, stdev)# Pick the correct answer.print("Which of the two choices is correct?")print("Choice 1 =", round(choice1,4))print("Choice 2 =", round(choice2,4))

Answer 1

Answer:

Explanation:

print("Confidence Interval for Average Relative Skill in the years 2013 to 2015")

print("------------------------------------------------------------------------------------------------------------")

# Mean relative skill of all teams from the years 2013-2015

mean = your_years_leagues_df['elo_n'].mean()

# Standard deviation of the relative skill of all teams from the years 2013-2015

stdev = your_years_leagues_df['elo_n'].std()

n = len(your_years_leagues_df)

#Confidence interval

stderr = stdev/(n ** 0.5) # variable stdev is the calculated the standard deviation of the relative skill of all teams from the years 2013-2015

# Calculate the confidence interval

# Confidence level is 95% => 0.95

# variable mean is the calculated the mean relative skill of all teams from the years 2013-20154

# variable stderr is the calculated the standard error

conf_int_95 = st.norm.interval(0.95, mean, stderr)

print("95% confidence interval (unrounded) for Average Relative Skill (ELO) in the years 2013 to 2015 =", conf_int_95)

print("95% confidence interval (rounded) for Average Relative Skill (ELO) in the years 2013 to 2015 = (", round(conf_int_95[0], 2),",", round(conf_int_95[1], 2),")")

print("\n")

print("Probability a team has Average Relative Skill LESS than the Average Relative Skill (ELO) of your team in the years 2013 to 2015")

print("----------------------------------------------------------------------------------------------------------------------------------------------------------")

mean_elo_your_team = your_team_df['elo_n'].mean()

# Calculates the probability a Team has Average Relative Skill GREATER than or equal to the Average Relative Skill (ELO) of your team in the years 2013 to 2015

choice1 = st.norm.sf(mean_elo_your_team, mean, stdev)

# Calculates the probability a Team has Average Relative Skill LESS than or equal to the Average Relative Skill (ELO) of your team in the years 2013 to 2015

choice2 = st.norm.cdf(mean_elo_your_team, mean, stdev)

# Pick the correct answer.

print("Which of the two choices is correct?")

print("Choice 1 =", round(choice1,4))

print("Choice 2 =", round(choice2,4)) # This is correct