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IT 403 -- Project 4
Probability and Tests for Proportions
Show all of you work for full credit.
- 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 in favor of the Safe Roads Ammendment, which is on the
November ballot in Illinois?
Flipping a coin or rolling a die is not allowed for Part 1.
Then answer these questions
- Describe what your dataset is and how you collected it. Are there are
any factors (lurking variables) that might have influenced your results?
- 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
SES = √n*phat*(1-phat).
- Roll a die 30 times, keeping track of the number of aces (ones) obtained.
Then answer these questions:
- Find a 95% confidence interval for the true probability of rolling
an ace. p is unknown, so use the estimated p of S / n, in the formula for
SES = √n*phat*(1-phat).
- Perform a formal test of hypotheses for testing whether the die is
fair for rolling an ace. Use the null hypotheses value of p for computing
the standard error for S.
- Use SPSS to simulate rolling a die 1,200 times. Use a Bernoulli
random variable where p = 1/6. Count the number of
ones obtained.
p is unknown, so use the estimated p of S / n, in the formula for
SES = √n*phat*(1-phat).
- Find a 95% confidence interval for the true probability of obtaining a 1.
- Perform a formal test of hypotheses for testing whether the true
probability of obtaining a 1 is 1/6. Use the null hypothesis value of p
for computing the standard error for S.