A survey was conducted to determine if adults in the US Fran

A survey was conducted to determine if adults in the U.S., France, and Germany believed humans contribute to global warming. Of 1125 adults in the U.S., 68% believed humans contribute to global warming, of 984 adults in France, 74% believed humans contribute to global warming, and of 2707 adults in Germany, 78% believed humans contribute to global warming. (Note: Two proportions may possibly be equal if their confidence intervals overlap.)

A) Construct a 99% confidence interval for the proportion of adults from the U.S. who say that humans contribute to global warming.

B) Construct a 99% confidence interval for the proportion of adults from France who say that humans contribute to global warming.

C) Construct a 99% confidence interval for the proportion of adults from Germany who say that humans contribute to global warming.

D) Based on your results for questions A and B, is it possible that the proportion for adults in the U.S. may equal the proportion of adults in France?

E) Based on your results for questions B and C, is it possible that the proportion for adults in France may equal the proportion of adults in Germany?

F) Based on your results for questions A and C, is it possible that the proportion for adults in the U.S. may equal the proportion of adults in Germany?

Solution

99% confidence interval for P given by

p± 2.58pq/n

U.S : n = 1125 p = 0.68 q = 0.32

p± 2.58pq/n

0.68± 2.58(0.68)(0.32)/1125

0.68± 0.0359

(0.6441 , 0.7159)

France : n = 984 p = 0.74   q = 0.26

p± 2.58pq/n

0.74± 2.58(0.74)(0.26)/984

0.74± 0.0361

(0.7039, 0.7761)

Germany :   n = 2707 p = 0.78   q = 0.22

p± 2.58pq/n

0.78± 2.58(0.78)(0.22)/2707

0.78± 0.0205

(0.7595 , 0.8005)

comparing A and B it is possible that the proportion for adults in U.S is some what equal to France

comparing B and C it is possible that the proportion for adults in France is some what equal to Germany

comparing A and C it is possible that the proportion for adults in U.S is some what equal to Germany