Assuming that all necessary conditions are met, what needs to be changed in the formula , so that we can use it to construct a confidence interval estimate for the population proportion p? A) The p̂ should be replaced by p. B) The t_a should be replaced by z_a. C) The t_a should be replaced by t_a/2. D) The t_a should be replaced by z_a/2. E) The p̂ should be replaced by z_a/2.

Question

Quizplus · Accepted Answer

To construct a confidence interval estimate for the population proportion p, we need to use the formula: p̂ ± t_a √((p̂(1-p̂))/n) However, since the sample size is large (assuming all necessary conditions are met), we can use the normal distribution instead of the t-distribution. This means we need to replace t_a with z_a/2, which gives us: p̂ ± z_a/2 √((p̂(1-p̂))/n) Therefore, the correct choice is D, which suggests replacing t_a with z_a/2.

Assuming That All Necessary Conditions Are Met, What Needs to Be