A poll taken by the General Social Survey in 2010 asked people in the United States whether they were satisfied with their financial situation. A total of 478 out of 2038 people said they were satisfied. The same question was asked in 2014, and 698 out of 2532 people said they were satisfied.

a. Construct a 95% confidence interval for the difference between the proportion of adults who said they were satisfied in 2014 and the proportion in 2010.

b. A sociologist claims that the proportion of people who are satisfied increased from 2010 to 2014 by more than 0.05. Does the confidence interval contradict this claim?