A 2010 poll asked people in the United States whether they were satisfied with their financial situation. A total of 303 out of 1158 people said they were satisfied. The same question was asked in 2012, and 339 out of 830 people said they were satisfied.

Part 1 of 2
(a) Construct a 98% confidence interval for the difference between the proportions of adults who said they were satisfied in 2012 and 2010. Let p₁ denote the proportion of individuals satisfied with their financial situation in 2012 and p₂ denote the proportion of individuals satisfied with their financial situation in 2010. Round the answers to three decimal places.

Part 2 of 2 (b) A sociologist claims that the proportion of people who are satisfied increased from 2010 to 2012 by more than 0.107. Does the confidence interval contradict this claim?