The General Social Survey is conducted every year and asks a variety of questions to a representative sample of non-institutionalized adults in the United States. In 2014, the survey showed that 45.6% of the 2,538 respondents said they were married. Forty years earlier, in 1974, the results showed that 77.8% of the 1,484 respondents said they were married. We want to calculate a 99% confidence interval for the difference in the proportions in the population that are married to compare the two time periods. 

a. Describe the parameter we want to estimate and assign appropriate symbols to it. 

b. Are the validity conditions met for this method? Explain. 

c. Find the theory-based 99% confidence interval. 

d. Interpret the confidence interval you obtained in the context of the study.