A random sample of high school students were asked, “What is your favorite season?” Out of 468 students in Florida, 149 said winter, whereas only 76 out of 458 from New York said winter. We want to determine a 95% confidence interval for the difference in the proportions of students in the populations of Florida and New York who prefer winter. 

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

b. Are the validity conditions met for a theory-based interval? Explain. 

c. Find the theory-based 95% confidence interval. 

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