Is College Worth It? In the New York Times article “College Graduates Fare Well in Jobs Market, Even through Recession,”

C. Rampell noted that college graduates have suffered through the recession and lackluster recovery with remarkable resilience. Of a random sample of 1020 college graduates, 35 were unemployed;

and of a random sample of 1008 high-school graduates (no college), 69 were unemployed.

a. At the 1% significance level, do the data provide sufficient evidence to conclude that college graduates have a lower unemployment rate than high-school graduates?

b. Find and interpret a 98% confidence interval for the difference in unemployment rates of college and high-school graduates.

Extending the Concepts and Skills Two-Proportions Plus-Four z-Interval Procedure. To obtain a plus-four z-interval for the difference between two population proportions, we first add one success and one failure to each of our two samples of data (hence, the term “plus four”) and then apply Procedure 12.4 on page 588 to the new data. In other words, in place of pˆ1 (which is x1/n1), we use p˜1 = (x1 + 1)/(n1 + 2), and in place of pˆ2 (which is x2/n2), we use p˜2 = (x2 + 1)/(n2 + 2). Thus, for a confidence level of 1 − α, the plus-four z-interval for p1 − p2 has endpoints

(p˜1 − p˜2) ± zα/2 ·



p˜1(1 − p˜1)

n1 + 2 + p˜2(1 − p˜2)

n2 + 2 .

As a rule of thumb, the two-proportions plus-four z-interval procedure can be used when both sample sizes are 5 or more.