Question

12

In a survey on supernatural experiences, 718 of 4019 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 the 4019 people were surveyed at a supernatural convention.

We need to assume that there are only 718 adult Americans.   

We need to assume that the 718 people are the only Americans who had seen or been with a ghost.

We need to assume that the 4019 people formed a random sample of adult Americans.

(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 who have seen or been with a ghost is within this interval.

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

Answer 1

Solution :

Given that,

n = 4019

x = 718

Point estimate = sample proportion = = x / n = 718 / 4019 = 0.179

1 - = 1 - 0.179 = 0.821

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.05 0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 ((( 0.179 * 0.821) / 4019 )

= 0.010

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.179 - 0.010 < p < 0.179 + 0.010

0.169 < p < 0.189

( 0.169 , 0.189 )

The 90% confidence interval for the population proportion p is : ( 0.169 , 0.189 )

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.