Random Thoughts 2012 (COMP 066)

1. Random Thoughts 2012(COMP 066) Jan-Michael Frahm Jared Heinly

2. Benford’s Law • 242 countries in the world • First digit of the population of each country

3. Benford’s Law • 242 countries in the world • First digit of the population of each country

4. Confidence Interval • Margin of error of N samples z*= Number of samples needed:

5. Average weight of population • Average weight deviation in preliminary experiment is σ=30 lb • Confidence level of 99% (z*=2.58) • How many do we need to ask to have a MOE of 2 lb?

6. What is a random sample? • Random subset of your test population • Randomly chosen voters, buyers, … • Sample represent the population • represents the student population of UNC • Which of these subsets are random? • All students in this class • Drawn by lottery from Connect Carolina • Students on the lawn • Random students asked at noon in Lenor Hall • ✗ • ✓ • ✗ • ✗

7. What can go wrong? Many factors can keep a poll from being a perfect indicator of how all of the people in the population think, feel, or behave. Here are just a few of the ways a poll can end up being a lot less than 100% accurate: • Phone book for selection of names at random to call • never question people with unlisted phone numbers or people who do not have a phone. • Research indicates that most phones are answered by women or older people. • interview only the people who answer, you will have a biased sample! • Phone leaves only small time frame (evening to reach people) • About 50% of registered voters do not vote • poll of 500 registered voters might not include anyone who votes • Almost any question will bias the answer to some degree. • For example, the pollsters might ask was Gandhi 110 when he died. Then ask what age did he die? The 110 will make the average higher.

8. Roulette Wheel example • How do we know about the MOE for the roulette wheel example? • Sampling all occurrences for each number over 5 days

9. How many trials? • Margin of error for a population proportion • Depends on proportion in the population that had the characteristic we searched for • Example: Over the 5 days of sampling we saw 52 occurrences of the 29 within the 1800 observed trials. We want 99% confidence level (z*=2.58). Hence 2.9% ±1% for 29 on the roulette wheel (1/37=2.7%)

10. Roulette wheel • How many trials do we need to have a 0.1% margin of error with a confidence level of 99% • z*=2.58 • the number of samples is

11. Election Polls • a margin of error states the confidence in the data collected • 70% of voters would choose Clinton, with a margin of error of +/- 5% • This doesn’t mean that another poll would also find 70% of voters for Clinton but surely another poll would end up somewhere between 65% (70%-5%) and 75% (70%+5%) • Depending on the demographics of the polled people • Is not the probability of an error in the poll is the variation due to the sampling

12. How many do you have to ask? • Example: Asked students in this course about the student body president vote they cast. 10 students Leimenstolland 5 students Lewis. We want 95% confidence level (z*=1.96). Hence 67% ±24% for Leimenstoll

13. UNC student elections • How many students do we need to ask to have a 1% margin of error with a confidence level of 95% • z*=1.96 • the number of samples is

14. UNC student body president election • How does this change with respect to the number of people asked