A Monster.com pool of 3,057 individuals asked, "What's the longest vacation you plan to take this summer?" The following relative frequency distribution summarizes the results. The 95% confidence interval for the proportion of people who plan a one-week vacation this summer is ________.
A) [0.345, 0.375]
B) [0.345, 0.382]
C) [0.343, 0.377]
D) [0.338, 0.382]

Question

A Monster.com pool of 3,057 individuals asked, "What's the longest vacation you plan to take this summer?" The following relative frequency distribution summarizes the results.  The 95% confidence interval for the proportion of people who plan a one-week vacation this summer is ________.
A) [0.345, 0.375] 
B) [0.345, 0.382] 
C) [0.343, 0.377] 
D) [0.338, 0.382]

Quizplus · Accepted Answer

To find the confidence interval for a proportion, we first need to calculate the sample proportion, which is the relative frequency of people who plan a one-week vacation this summer. From the table, the relative frequency for one week vacation is 0.36.

Next, we need to calculate the standard error of the proportion:

SE = sqrt(p*(1-p)/n)
SE = sqrt(0.36 * 0.64 / 3057)
SE = 0.013

To find the 95% confidence interval, we use the formula:

CI = p ± z*SE

where z is the z-score for a 95% confidence interval, which is 1.96.

CI = 0.36 ± 1.96*0.013
CI = [0.343, 0.377]

Therefore, the 95% confidence interval for the proportion of people who plan a one-week vacation this summer is [0.343, 0.377]. Option C is the closest choice.

A MonsterCom Pool of 3,057 Individuals Asked, "What's the Longest Vacation