Question
R Language code Suppose we are interested in P(A) for some event A. While the n^(1/2) rule is simple, a better 95% confidence interval is
R Language code
Suppose we are interested in P(A) for some event A. While the n^(1/2) rule
is simple, a better 95% confidence interval is given by
p +- 1.96((p(1-p)/n)^(1/2))
where ^p is still the proportion of times A occurs in our sample. This
confidence is smaller, which is better, but still contains the true probability
about 95% of the time.
Suppose our event of interest has P(A) = 1/10.
(a) Simulate 300 trials of the experiment and print out the resulting
confidence interval using the formula above.
(b) In your simulation above, for each trial, 1,. . . , 300, plot the upper
and lower endponts of the confidence interval. That is, if n is the
number of trials done so far, and un and ln are the upper and lower
limits of the confidence interval based on n trials, plot the points
(x; y ) = (n; Un ) and (x; y ) = (n; Ln ) for n = 1; : : : ; 300.
(c) Repeat the experiment above 1000 times and compute the fraction of
the time the confidence interval contains the true probability, 1/10.
This should happen about 95% of the time.
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