Question

1. Discuss the concept of a confidence interval estimate of the proportion. Include a discussion of:

(a) the impact changing the sample size has on the calculation of the CIE holding all other variables constant. (Discuss how the CIE will change as the sample size "n" changes and WHY);

(b) the impact of changing the level of confidence on the CIE holding all other variables constant. (Discuss how the CIE will change as the confidence level changes and WHY.).

Answer 1

(A) .as we seen in this formula as sample size n increses margin of error decreses reaulting width of confidence interval decreses and go towards better precision and for decrease in sample size increse the CI width and and go towards less precision.

B).

this is the general formula for CI of proportion

as formula (1-alpha )*100% is the confidence ,and alpha is a level of significance.

as the confidence level increses the value of z increses resulting margin of error increses and then confidence interval width also increses and it goes towards lesser precision. or vice versa

suppose we have confidence level 90% then the Z value from table for two tail is 1.645 and if confidence level is 95% the Z value for two tail from standard table is 1.96 ,this can be seen that Margin of error increses ,

then Obiviously confidence width increses by incresing of confidence level by keeping all other variable constant.

Thank you.