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Statistical Probabilities and Distributions
Homework for Prob./Dist. Lesson 13
- Given a 2003 penny data
sample mean of 15.8 and a sample standard deviation of 1.91
(with n=16), calculate the margin of error
(assume a 95% confidence interval will be generated).
- Given a sample mean of 15.8 and a sample standard deviation of 1.91
(with n=16), calculate a 95% confidence interval.
- Given a sample mean of 15.8 and a sample standard deviation of 1.91
(with n=16), calculate the margin of error
(assume a 99% confidence interval will be generated).
The appropriate z-score is 2.576.
- Given a sample mean of 15.8 and a sample standard deviation of 1.91
(with n=16), calculate a 99% confidence interval.
- A P-value is a way to express the confidence of our results.
For a one-tailed test,
it is the area under the curve to the right (or left) of our observed mean.
Calculate a z-score using our observed mean (15.8), expected mean (10.0),
and standard error (1.91/sqrt(16)) and sketch this region on a normal curve.
- Calculate this area by doing a normalcdf(z,9E99), where
z is the value calculated above.
- Alpha is the term used to express the level of significance we will
accept. For 95% confidence, alpha=0.05. If our P-value is less than alpha,
we can reject our null hypothesis (H0: µ=10).
Should we reject our null?
- Try to identify sources of error or bias which might account for these
(highly significant) results.
- Do you think other coins might display similar characteristics?
How many times would you have to test it to reach a significant conclusion.
- Do you think spinning coins (especially some of the new and
different state quarters) might display similar characteristics?
We may hand out a data gathering sheet with very specific collection
instructions.
- How willing are you to bet money using this
method of "flipping" a coin
(assuming you have no scruples against such an activity)?