USA Today reports that the average expenditure on Valentine's Day was expected to be $$100\mathrm{.}89.$ Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of $56$ male consumers was $$130\mathrm{.}01,$ and the average expenditure in a sample survey of $33$ female consumers was $$64\mathrm{.}39.$ Based on past surveys, the standard deviation for male consumers is assumed to be $$30,$ and the standard deviation for female consumers is assumed to be $$12.$ The $z$ value is $2\mathrm{.}576.$

Round your answers to $2$ decimal places.

a$.$ What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females?

b$.$ At $99\%$ confidence, what is the margin of error?

c$.$ Develop a $99\%$ confidence interval for the difference between the two population means. to