In 2006, the General Social Survey asked, "Do you see yourself as someone that tends to be lazy?" For this question, 20 people said that they definitely did out of 1513 randomly selected people. What is the 95% confidence interval for the proportion of all Americans that believe that believe that they tend to be lazy?

Question

In 2006, the General Social Survey asked, "Do you see yourself as someone that tends to be lazy?" For this question, 20 people said that they definitely did out of 1513 randomly selected people. What is the 95% confidence interval for the proportion of all Americans that believe that believe that they tend to be lazy?

Answer 1

Use a confidence interval formula for proportions:

CI95 = p + or - (1.96)(√pq/n)
...where √ = square root, p = x/n, q = 1 - p, and n = sample size.

Note:
x = 20
n = 1513

Remember to convert all fractions to decimals before calculating the interval.

I hope this will help.