In a survey of 1,000 people,420 are opposed to the tax increase.Construct a 95 percent confidence interval for the proportion of those people opposed to the tax increase.

Question

Quizplus · Accepted Answer

To construct a confidence interval for the proportion of people opposed to the tax increase, we can use the formula:
CI = p ± z*sqrt((p*(1-p))/n)
where 
p = sample proportion = 420/1000 = 0.42
n = sample size = 1000
z = z-score from the standard normal distribution for a 95% confidence level, which is 1.96.

Substituting these values, we get:
CI = 0.42 ± 1.96*sqrt((0.42*(1-0.42))/1000)
CI = [0.389, 0.451]

Therefore, the best choice is B, which matches the above calculated confidence interval.

In a Survey of 1,000 People,420 Are Opposed to the Tax