The ambient temperature in which humans are comfortable varies with culture, activity, metabolic rate, psychological state, environment, and season. For most people in the United States, the comfort...

The ambient temperature in which humans are comfortable varies with culture, activity, metabolic rate, psychological state, environment, and season. For most people in the United States, the comfort zone is 68 to 78°F. During a recent winter, a random sample of homeowners was selected from two different parts of the country. The thermostat temperature setting (in °F) was recorded for each home, and the summary statistics are given in the following table.

a. Find a 95% confidence interval for the true mean thermostat setting for New England homeowners during winter.

 b. Find a 95% confidence interval for the true mean thermostat setting for Southern homeowners during winter.

c. What assumption(s) did you make in constructing these two confidence intervals?

d. Using your answers to parts (a) and (b), is there any evidence to suggest the New England mean thermostat setting is different from the Southern thermostat setting during winter? Justify your answer.