Question

In the Python script, you calculated a 95% confidence interval for the average relative skill of all teams in the league during the years of your team. Additionally, you calculated the probability that a given team in the league has a relative skill level less than that of the team that you picked.

Info here:

Confidence Level (%)	Confidence Interval
95%	2013 to 2015 – 1502.02 (Rounded)
95%	2013 to 2015 – 1502.02, 1507.18 (Unrounded)

**Probability a team has Average Relative Skill less than the Average Relative Skill(ELO) of Bulls : 0.6513

• Provide a detailed interpretation of the confidence interval in terms of the average relative skill of teams in the range of years that you picked.
• How would your interval be different if you had used a different confidence level?
• What is the probability that a given team in the league has a relative skill level less than that of the team that you picked? Is it unusual that a team has a skill level less than your team?

Can you please help with the 3 bullet questions above? Many thanks! :)

Answer 1

Interpretation : We are 95% confident that the average relative skill level of the teams in league is between 1502.02 and 1507.18.

If we change confidence level to higher value say 99% then the new interval will be wider and if we change the confidence level to lower value say 90% then the new interval will be narrower than current one. This is because confidence interval has formula :  

the probability that a given team in the league has a relative skill level less than that of the team that you picked = 0.6513

No, it is not unusual for a given team to have less relative skill because probability for this happening is 0.6513 i.e. it is more likely than not for a team to be having less relative skill than the picked team. OR 65% of the team have skill less than my team.