A travel article researcher randomly sampled 250 adult residents of Illinois and asked each resident if he/she planned to vacation outside of Illinois this coming summer.Fifty-six of these adults responded that they plan to vacation outside of Illinois.What is the 95% confidence interval for the population proportion of adult residents of Illinois who plan to vacation outside of Illinois this coming summer?
A)(0.178, 0.318)
B)(0.246, 0.250)
C)(0.172, 0.276)
D)(0.142, 0.354)

Question

Quizplus · Accepted Answer

To find the confidence interval for the population proportion, we can use the formula:
p̂ ± z*(√(p̂(1-p̂)/n))
where p̂ is the sample proportion, z* is the z-score for the desired confidence level (95% in this case), and n is the sample size.
Plugging in the given values, we get:
p̂ = 56/250 = 0.224
z* for 95% confidence level is 1.96
n = 250
Calculating the interval using the formula, we get:
0.224 ± 1.96*(√((0.224)(1-0.224)/250)) = (0.172, 0.276)
Therefore, choice C is the correct confidence interval.

A Travel Article Researcher Randomly Sampled 250 Adult Residents of Illinois