From a survey of coworkers you find that 32% of 150 have already received this year's flu vaccine. An approximate 98% confidence interval is (0.231, 0.409). a) How would the confidence interval change if the sample size had been 600 instead of 150? b) How would the confidence interval change if the confidence level had been 90% instead of 98%? c) How would the confidence interval change if the confidence level had been 99% instead of 98%?

a) Narrower

b) Narrower

c) Wider            

Step-by-step explanation:

We are given the following in the question:

Proportion of coworker who received flu vaccine = 32%

98% confidence interval: (0.231, 0.409)

Confidence interval:

a) Sample size had been 600 instead of 150

If we increase the sample size, thus the standard error of the interval decreases.

Since the standard error decreases, the confidence interval become narrower.

b) Confidence level had been 90% instead of 98%

As the confidence level increases, the confidence interval becomes narrower. This is due to a smaller value of z-statistic at 90% confidence level.

c) Confidence level had been 99% instead of 98%

As the confidence level increases, the width of the confidence interval increases and the confidence interval become wider. This is because of a larger value of z-statistic at 99% confidence interval.