Question: Suppose X1,...,Xn is a random sample from a Bernoulli(p) distribution and the sample average is xn = 0.45, based on which we can construct a

Suppose X1,...,Xn is a random sample from a Bernoulli(p) distribution and the sample average is xn = 0.45, based on which we can construct a 95% confidence interval for p. Now we collect more data and the sample average is around 0.48, we want to construct a 90% confidence interval with the length being 1/3 of the 95% one. How large should the sample size nnew be in terms of n

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