Question: Is it true that for a given sample size, n, an increase in confidence is achieved by widening (and making less precise) the confidence interval?

Is it true that for a given sample size, n, an increase in confidence is achieved by widening (and making less precise) the confidence interval?

Why is the sample size needed to determine the proportion smaller when the population proportion is 0.20 than when the population proportion is 0.50?

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