Question

Discuss how each of the following will affect the width of a confidence interval for estimating a population proportion (in each case assume all other values remain constant):

a) An increase in sample size used to find pˆ

b) A higher confidence level

Answer 1

a.)Confidence Interval:

So, lower and upper limit of the confidence interval will decrease.

b.)as we know

Critical value at 95% confidence=1.96

critical value at 98% confidence=2.33

Critical value at 99% confidence=2.58

so, when confidence level increases due to that the Margin of error part

will increase, as Margin of error increase the width of the confidence interval increases.