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IT 223 -- Project 4

Probability and Tests for Proportions

Show all of you work for full credit.

1. Think of a random process that can be modeled as a Bernoulli random variable. Collect 30 or more observations. Here are some suggestions:
   
   • Perform some sports activity like shooting free throws from 15 feet, kicking field goals, putting, chipping, or driving a golf ball close to a target.
   • Interview people on a street, asking each of them a yes-or-no question like are you in favor of converting to the metric system, are you in favor of immigration reform, do you think that the Chicago should make another bid for the Olympics, are you right handed (vs. left-handed or ambidextrous)?
   • Find a street intersection where cars driving in to the intersection must either turn left or right. Consider left as 0 and right as 1.
   Flipping a coin or rolling a die is not allowed for Part 1.
   Then answer these questions
   
   1. Describe what your dataset is and how you collected it. Are there are any factors (lurking variables) that might have influenced your results?
   2. Find a 95% confidence variable for the true probability p. p is unknown, so use the estimated p of S / n, in the formula for SE_S = √n*phat*(1-phat).
2. Roll a die 30 times, keeping track of the number of aces (ones) obtained. Then answer these questions:
   
   1. Find a 95% confidence interval for the true probability of rolling an ace. p is unknown, so use the estimated phat of S / n, in the formula for SE_S = √n*phat*(1-phat).
3. Simulate rolling a die 1,200 times using the R function binom. p is unknown, so use the estimated p of S / n, in the formula for SE_S = √n*phat*(1-phat).
   
   1. Find a 95% confidence interval for the true probability of obtaining a 1.