A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate A. The 95% confidence interval for the true proportion of people who favors Candidate A is
A)0.419 to 0.481
B)0.40 to 0.50
C)0.45 to 0.55
D)1.645 to 1.96

Question

Quizplus · Accepted Answer

We can use the formula for calculating the confidence interval for a proportion given by:

CI = p ± z*sqrt((p(1-p))/n)

Where, 
p = sample proportion = 450/1000 = 0.45
z = z-value for 95% confidence level = 1.96 (approx.)
n = sample size = 1000

Plugging in the values, we get:

CI = 0.45 ± 1.96*sqrt((0.45(1-0.45))/1000)
CI = 0.45 ± 0.031
CI = (0.419, 0.481)

Therefore, the 95% confidence interval for the true proportion of people who favor Candidate A is 0.419 to 0.481, and the best choice is A.

A Random Sample of 1000 People Was Taken