Why do we subtract 0.5/N from the lower limit and add 0.5/N to the upper limit when computing a confidence interval for the population proportion?
true
true
We need to correct for the fact that we are approximating a discrete distribution (the sampling distribution of p) with a continuous distribution (the normal distribution).
false
The estimate of the population proportion is slightly biased, and we need to correct for it.
false
The estimate of the standard error is slightly biased, and we need to correct for it.
We make these corrections because we approximate a discrete distribution with a continuous one.
The newspaper conducted a survey and asked some of the city's voters which candidate they preferred for mayor. The surveyors computed a 95% confidence interval and found that the percent of the voters in the city who prefer Candidate A ranges from 51% to 59%. What is the margin of error (as a percent)?
4
0.00
Because the confidence interval ranges from 51% to 59%, the newspaper must have found that 55% of their sample prefer Candidate A. Because the confidence interval extends 4% in both directions, the margin of error is 4%.
A researcher was interested in knowing how many people in the city supported a new tax. She sampled 100 people from the city and found that 40% of these people supported the tax. What is the upper limit of the 95% confidence interval on the population proportion?
.501
0.002
The standard error is sqrt[(.4)(.6)/100] = .0490. The correction = .5/100 = .005. Thus, the upper limit of the 95% confidence interval is: .4 + (1.96)(.049) + .005 = .501. Clearly, there is a large margin of error.