Question

From a survey of coworkers you find that 56​% of 150 have already received this​ year's flu vaccine. An approximate 98​% confidence interval is ​(0.466, 0.654​).

​a) How would the confidence interval change if the sample size had been 2400 instead of 150​?

​b) How would the confidence interval change if the confidence level had been 99​% instead of 98​%?

​c) How would the confidence interval change if the confidence level had been 95​% instead of 98​%?

Answer 1

a)

Increasing the sample size will decrease the width of Confidence Interval and hence it will narrows the CI

b)

Increasing the confidence level to 99% will increase the value of z from 2.33 to 2.58 and hence this will widen the CI

c)

Decreasing the confidence level to 95% will decrease the value of z from 2.33 to 1.96 and hence this will narrows the CI