First, this section shows how to compute a confidence interval for Pearson's correlation. The solution uses Fisher's z transformation. Then, it explains the procedure to compute confidence intervals for population proportions where the sampling distribution needs a normal approximation.
Proportion
Questions
Question 1 out of 3.
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?
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).
The estimate of the population proportion is slightly biased, and we need to correct for it.
The estimate
Question 2 out of 3. 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)?
Question 3 out of 3.
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?