A Confidence Interval for MJ's Career Scoring Average
The question of this analysis is to find a confidence interval for Michael Jordan's career scoring average. We have the data for his last fifteen games starting from December 5, 1996. They were,
| Opponent | Points |
| Los Angeles Clippers | 20 |
| Millwaukee | 40 |
| San Antonio | 35 |
| Dallas | 36 |
| Los Angeles Clippers | 40 |
| Utah | 44 |
| Denver | 31 |
| Phenoix | 37 |
| Atlanta | 25 |
| Charlotte | 38 |
| Miami | 28 | >
| Phenoix | 26 | >
| Boston | 27 |
| Detroit | 15 | >
| Miami | 50 | >
Use this data, enter in the spreadsheet "Day 5-CI" and answer the following questions.
- What are two assumptions that are being made about the data that allows us to use the BOOTSTRAP method?
- Discuss the randomness of the data. Could a better sample have been obtained? Is this sample an accurate representation of Jordan's career?
- Enter the sampling rate in cell C2. This tells the spreadsheet how many sample to take from the data. Generally, the rate is the same as how many data points there are.
- Run ten trials and answer the following.
- What is the range of means you get?
- What is the median of the trials?
- How much variability is there in your range?
- What do you think this will tell us about the range of the confidence interval?
- Why is it important that we now run more trials?
- Develop a confidence interval based on 50 trials.
- Determine an appropriate level of significance (5-95, 2.5-97.5, etc..) and explain why you choose it.
- What does this make your confidence interval?
- Develop three more confidence intervals and discuss how they compare to each other.
- Now, develop a confidence interval based on 100 trials. Use the same level of significance that you used in the previous problem.
- Again, develop three more intervals and discuss how they compare to each other.
- Is there any difference between the intervals with 100 trials compared to those of 50 trials.
- What would we expect to happen to our interval if we run more and more trials (i.e., 1000).
- If we had Jordan's points scored from his last 100 games, what would we expect to happen to our confidence intervals?
- If Jordan's career average had been 34 points a game before this year is there proof to support the statement, "Michael Jordan has not been scoring as many points as he used to"? Why or why not?
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