In a survey on supernatural experiences, 722 of 4005 adult Americans surveyed reported that they 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.)
To construct a confidence interval for a proportion, we can use the following formula:
CI = p̂ ± Z * √(p̂(1-p̂)/n),
where p̂ is the sample proportion, Z is the z-score corresponding to the desired confidence level, and n is the sample size.
Given that 722 out of 4005 adult Americans surveyed reported supernatural experiences, we can calculate the sample proportion as the ratio of the number of people who reported supernatural experiences to the total sample size:
p̂ = 722 / 4005 = 0.1804.
To determine the z-score for a 90% confidence level, we need to find the value that corresponds to 0.05 (half of 1 minus the desired confidence level) in the standard normal distribution table. The z-score for 0.05 is approximately 1.645.
Now we can calculate the margin of error (ME) using the formula:
ME = Z * √(p̂(1-p̂)/n),
ME = 1.645 * √(0.1804 * (1-0.1804) / 4005),
ME ≈ 0.0131.
Finally, we can construct the confidence interval by subtracting and adding the margin of error from the sample proportion:
CI = 0.1804 ± 0.0131.
Rounded to three decimal places, the confidence interval for the proportion of adult Americans who have seen or been with a ghost is approximately:
CI = (0.167, 0.193).