Question: 5. For a binomial proportion, a $95 %$ confidence interval contains all values $p_{0}$ for which the two-sided p-value exceeds $0.05$ i.e. each of the

5. For a binomial proportion, a $95 %$ confidence interval contains

5. For a binomial proportion, a $95 %$ confidence interval contains all values $p_{0}$ for which the two-sided p-value exceeds $0.05$ i.e. each of the one-sided p-values exceeds $0.025$. Therefore on observing $X=r$ the exact $95 %$ confidence interval for $\mathrm{p}$ is $\left(p_{1}, p_{u} ight) $ such that $$ P\left(X \leq r \mid p_{1} ight)=0.025 and $$ P\left(X \geq r \mid p_{u} ight)=0.025 $$ Suppose we observe 8 successes in 10 trials. Find a confidence interval for $p$ with confidence coefficient as close as possible to $95 %$. Use binomial tables. SP.PB.093

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