One in five 18-year-old Americans has not graduated from high school (The Wall Street Journal, April 19, 2007). A mayor of a northeastern city comments that its residents do not have the same graduation rate as the rest of the country. An analyst from the Department of Education decides to test the mayor’s claim. In particular, she draws a random sample of 80 18-year-olds in the city and finds that 20 of them have not graduated from high school.
a. Compute the point estimate for the proportion of 18-year-olds who have graduated from high school in this city.
b. Use this point estimate to derive the 95% confidence interval for the population proportion.
c. Can the mayor’s comment be justified at 95% confidence?