# Project #46877 - Frequentist Statistical Methods

Consider the data set 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, and 0 assumed produced as an iid sample of n = 20 obervations. Do and show R code for all.

A. What distribution produced these data? Give the distribution in list form, as well as its mean, variance, and standard deviation.

B. Give the bootstrap distribution for these data in list form, as well as its mean, variance, and standard deviation. Explain why the distribution in Exercise A is different from the bootstrap distribution.

C. Give the approximate 95% interval for the mean of the distribution in Exercise A using the formula: y bar ± 1.96$\hat{\sigma }$$\sqrt{n}}$ where $\hat{\sigma }$ is the plug-in estimate from Exercise B.

D. Statistics sources give the approximate 95% confidence interval for the Bernoulli parameter $\pi$ as $\hat{\pi }$ ± 1.96$\sqrt{\hat{\pi }(1-\hat{\pi })/n}$. Show that your interval in Exercise C is identical to this Bernoulli confidence interval. (If you are mathematically inclined, prove they are the same for general data.)

E. Is $\pi$ in your confidence interval of Exercise C? Explain carefully, like a good frequentist.

F. Generate 10,000 sample of n = 20 each from the Bernoulli(0.6) distribution to estimate the true confidence level of this procedure . Is it reasonably close to 95%? How about when $\pi$ = 0.01?

 Subject Mathematics Due By (Pacific Time) 11/11/2014 10:00 pm
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