Question

Consider the formula used for any confidence interval and the elements included in that formula. What happens to the confidence interval if you (a) increase the confidence level, (b) increase the sample size, or (c) increase the margin of error? Only consider one of these changes at a time. Explain your answer with words and by referencing the formula.

Answer 1

Formula used for confidence interval

where, = sample mean

s = standard deviation of mean

n = sample size

= critical value for confidence level

(a) increase the confidence level

If confidence level is increase the value of increase

term increases

Hence, confidence interval increase

(b) increase the sample size

If sample size increase

term decreases

Hence, confidence interval decrease

(c) increase the margin of error

margin of error =

Therefore, confidence interval increase