Question

From a survey of coworkers you find that 51​% of 150 have already received this​ year's flu vaccine. An approximate 95​% confidence interval is ​(0.428​,0.592​). Which of the following are​ true? If​ not, explain briefly. ​a) 95​% of the coworkers fall in the interval ​(0.428​,0.592​). ​b) We are 95​% confident that the proportion of coworkers who have received this​ year's flu vaccine is between 42.8​% and 59.2​%. ​c) There is a 95​% chance that a randomly selected coworker has received the vaccine. ​d) There is a 51​% chance that a randomly selected coworker has received the vaccine. ​e) We are 95​% confident that between 42.8​% and 59.2​% of the samples will have a proportion near 51​%.

Answer 1

#The correct Satatement for 95 % CI for population proportion

given that :

# 95​% confidence interval is a ​(0.428​,0.592​)

(a)

It is not correct becuase it says that 95​% of the coworkers fall in the interval ​while confidence interval says that we are 95% confident that the proprotion of coworkers that have already received this​ year's flu vaccine lie in the interval (0.428, 0.592).

(b)

It is true.

(c)

The given confidence interval is says about the proprotion of coworkers that have already received this​ year's flu vaccine. But given explanation told about a single coworker.

(d)

There should be 95% instead of 51% chance.

(e)

Confidence interval give interpretation about population parameter not about sample statistics.

#Only STATEMENT B in the list here is true.