A manager at a market research firm randomly sampled 254 adult residents of Ohio and asked each resident if he/she planned to vacation outside of Ohio this coming summer.Sixty-three of these adults responded that they plan to vacation outside of Ohio this coming summer.What is the 95% confidence interval for the population proportion of adult residents of Ohio who plan to vacation outside of Ohio this coming summer?
A) (0.178, 0.318)
B) (0.246, 0.250)
C) (0.195, 0.301)
D) (0.142, 0.354)

Question

Quizplus · Accepted Answer

To calculate the confidence interval for the population proportion, we can use the following formula:

CI = p̂ ± z*√[(p̂(1-p̂))/n]

where p̂ is the sample proportion (63/254 = 0.248), z is the z-value for the desired confidence level (95% → z = 1.96), and n is the sample size (254).

Plugging in the values, we get:

CI = 0.248 ± 1.96*√[(0.248(1-0.248))/254]
   = 0.248 ± 0.053
   = (0.195, 0.301)

Therefore, the 95% confidence interval for the population proportion of adult residents of Ohio who plan to vacation outside of Ohio this coming summer is (0.195, 0.301). The best choice is (C).

A Manager at a Market Research Firm Randomly Sampled 254