Question

In March 2015, the Public Policy Institute of California (PPIC) surveyed 7525 likely voters living in California. This is the 148th PPIC research poll, and is part of a survey series that started in 1998. PPIC researchers find that 3266 survey participants are registered Democrats and 2137 survey participants are registered Republicans. PPIC is interested in the difference in approval rate for the governor between registered Democrats and registered Republicans in California. Participants were asked: “Overall, do you approve or disapprove of the way the governor of California is handling his job?” 2450 of the registered Democrats answered “Yes” and 684 of the registered Republicans answered “Yes.” True or false? A normal model is an appropriate fit for the sampling distribution of sample differences.

A) True

B) False

Answer 1

expected successes and failures in both samples at least 10 then difference in proportions follows normal distribution.that is

n1p1>=10

n1(1-p1)>10

n2p2>10

n2(1-p2>10

n1p1=3266 *2450 /3266 =2450>10

n1*(1-p1)=3266(1-2450/3266)>10

n2p2=2137*684 /2137=684>10

n2(1-p2)=2137*(1-684/2137)= 1453>=10

SO

follows normal distribution

ANSWER:

A) True