If recent work produced the confidence interval $p \in(0.3355,0.4223)$, then what should we use as a conservative guess for the value of $p$ when computing sample size?
Answer
Final Answer: The conservative guess for the value of $p$ when computing sample size is \(\boxed{0.4223}\)
Step 1 ：The conservative guess for the value of $p$ when computing sample size would be the value that maximizes the sample size. In the case of a binomial proportion, the sample size is maximized when $p=0.5$. However, since $0.5$ is not in the given confidence interval $(0.3355,0.4223)$, we should use the endpoint of the interval that is closest to $0.5$, which is $0.4223$.
Step 2 ：So, the conservative guess for the value of $p$ when computing sample size is $p = 0.4223$
Step 3 ：Final Answer: The conservative guess for the value of $p$ when computing sample size is \(\boxed{0.4223}\)
