A travel article reasearcher 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

The formula for the confidence interval for a population proportion is:sample proportion +/- margin of errorwhere the margin of error is:z * sqrt((sample proportion * (1 - sample proportion)) / sample size)where z is the z-score corresponding to the desired confidence level. For a 95% confidence level, z = 1.96.Plugging in the values from the question, we get:0.56 +/- 1.96 * sqrt((0.56 * (1 - 0.56)) / 250)= 0.56 +/- 0.052= (0.172, 0.276)Therefore, the 95% confidence interval for the population proportion of adult residents of Illinois who plan to vacation outside of Illinois this coming summer is (0.172, 0.276).

A Travel Article Reasearcher Randomly Sampled 250 Adult Residents of Illinois