8 test Satisfied A po11 asked people in the United States wh

8 test Satisfied? A po11 asked people in the United States whether they were satisfied with the way things were going in the country. Of 830 people aged 18-29, 339 said they were satisfied. Of 1158 people aged 30 and older, 303 said they were satisfied. Part 1 out of 2 Construct a 98% confidence interval for the difference between the proportions of adults aged 18?29 and those 30 and older who are satisfied. Let p1 denote the proportion of people aged 18?29 who said they were satisfied with the way things were going. Round the answers to three decimal places. A 98% confident that the difference between the proportion of adults aged 18?29 and those 30 and older who are satisfied is

Solution

Given a=1-0.98=0.02, Z(0.01) = 2.33 (from standard normal table)

p1=339/830=0.4084337

p2=303/1158= 0.261658

So the lower bound is

(p1-p2)- Z*sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.4084337-0.261658)-2.33*sqrt(0.4084337*(1-0.4084337)/830+0.261658*(1-0.261658)/1158)

=0.097

So the upper bound is

(p1-p2)+ Z*sqrt(p1*(1-p1)/n1+p2*(1-p2)/n2)

=(0.4084337-0.261658)+2.33*sqrt(0.4084337*(1-0.4084337)/830+0.261658*(1-0.261658)/1158)

=0.197