Suppose that x = 21 is an observation from a B(27, p) random variable. (a) Compute a

Question:

Suppose that x = 21 is an observation from a B(27, p) random variable.
(a) Compute a two-sided 99% confidence interval for p.
(b) Compute a two-sided 95% confidence interval for p.
(c) Compute a one-sided 95'; confidence interval that provides a lower bound for p.
(d) Consider the hypotheses
H0: p < 0.6 versus HA: p > 0.6.
Calculate an exact p-value using the tail probability of the binomial and compare it with the corresponding /'-value calculated using a normal approximation.
Distribution
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