## Confidence Intervals for Correlation and Proportion

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?