Question

Let p1 represent the population proportion of U.S. senatorial and congressional (House of Representatives) Democrats who are in favor of a new modest tax on junk food. Let p2 represent the population proportion of U.S. senatorial and congressional Republicans who are in favor of a new modest tax on junk food. Out of the 265 Democratic senators and members of Congress, 106 of them are in favor of a junk food tax. Out of the 285 Republican senators and members of Congress, only 57 are in favor of a junk food tax. Find a 95 percent confidence interval for the difference between proportions l and 2.

Answer 1

Sample proportion 1 = 106 / 265 = 0.4

Sample proportion 2 = 27 / 285 = 0.2

95% confidence interval for p1 - p2 is

(1 - 2) - Z * sqrt [ (1 ( 1 - 1) / n1) + (2 ( 1 - ​2) / n2) ]   < p1 - p2 <

(1 - 2) - Z * sqrt [ (1 ( 1 - 1) / n1) + (2 ( 1 - ​2) / n2) ]

(0.4-0.2) - 1.96 * sqrt [ ( 0.4 * 0.6 / 265) + ( 0.2* 0.8 / 285) ] < p1 - p2 <

(0.4-0.2) - 1.96 * sqrt [ ( 0.4 * 0.6 / 265) + ( 0.2* 0.8 / 285) ]

0.2 - 0.075 < p1 - p2 < 0.2 + 0.075

0.125 < p1 - p2 < 0.275

95 % CI is ( 0.125 , 0.275)