Question

In a survey on supernatural experiences, 724 of 4003 adult Americans surveyed reported that they had seen or been with a ghost.

(a) What assumption must be made in order for it to be appropriate to use the formula of this section to construct a confidence interval to estimate the proportion of all adult Americans who have seen or been with a ghost?

We need to assume that there are only 724 adult Americans.We need to assume that the 4003 people were surveyed at a supernatural convention.    We need to assume that the 4003 people formed a random sample of adult Americans.We need to assume that the 724 people are the only Americans who had seen or been with a ghost.

(b) Construct a 90% confidence interval for the proportion of all adult Americans who have seen or been with a ghost. (Round your answers to three decimal places.)
(  ,  )

Interpret the interval.

We are 90% confident that the proportion of all adult Americans who have seen or been with a ghost is within this interval.We are 90% confident that the proportion who have seen or been with a ghost is within this interval.    We are confident that the proportion of all adult Americans who have seen or been with a ghost is within this interval 90% of the time.We are confident that 90% of the proportion of all adult Americans who have seen or been with a ghost is within this interval.

(c) Would a 99% confidence interval be narrower or wider than the interval computed in part (b)?

narrowerwider   

Answer 1

a) The assumption must be made in order for it to be appropriate to use the formula of this section to construct a confidence interval to estimate the proportion of all adult Americans who have seen or been with a ghost :

We need to assume that the 4003 people formed a random sample of adult Americans.

b) Here

sample proportion

and sample size

a 90% confidence interval for the proportion of all adult Americans who have seen or been with a ghost

Interpretation : We are 90% confident that the proportion who have seen or been with a ghost is within this interval.

c) Since confidence coefficient of 99% confidence interval > confidence coefficient of 95% confidence interval,

so the interval would be wider.