From a survey of coworkers you find that 48% of 200 have already received this year's flu vaccine. A 95% confidence interval is (0.409, 0.551).

Which of the following (a - e) are true?

a) 95% of the coworkers fall in the interval (.409, .551).

b) we are 95% confident that the proportion of coworkers who have received this year's flu vaccine is between 40.9% and 55.1%.

c) There is a 95% chance that a random selected coworker has received the vaccine.

d) There is a 48% chance that a random selected coworker has received the vaccine.

e) We are 95% confident that between 40.9% and 55.1% of the sample will have a proportion near 48%.

How would the confidence interval change if the sample size had been 800 instead of 200?

Would the confidence interval become smaller or larger if the confidence level had been 90% instead of 95%?

Would the confidence interval become smaller or larger if the confidence level had been 99% instead of 95%