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 the proportion of people who plan a one-week vacation this summer, we need to use the formula:
CI = p ± z*√((p(1-p))/n)
Where:
p = proportion of people who plan a one-week vacation
n = sample size
z = z-score corresponding to the level of confidence (95% confidence = 1.96)
First, we need to find the values for p and n from the given data:
p = 960/3057 = 0.314
n = 3057
Now, we can calculate the confidence interval:
CI = 0.314 ± 1.96√((0.314(1-0.314))/3057)
CI = 0.314 ± 0.017
CI = [0.297, 0.331]
This means we can be 95% confident that the true proportion of people who plan a one-week vacation this summer is between 0.297 and 0.331. However, none of the given answer choices match exactly with this interval. The closest answer choice is C, which has an interval of [0.343, 0.377]. This interval does not overlap with the calculated interval, but it is the closest option. Therefore, the best choice is C.

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