Exercise $10\mathrm{.}05$ Algo $($Inferences About the Difference Between Two Population Means: Sigmas Known$)$

Question $2$ of $14.$

Hint$($s$)$ Check My Work

USA Today reports that the average expenditure on Valentine's Day was expected to be $$100\mathrm{.}89.$ Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of $48$ male consumers was $$138\mathrm{.}54,$ and the average expenditure in a sample survey of $33$ female consumers was $$61\mathrm{.}81.$ Based on past surveys, the standard deviation for male consumers is assumed to be $$32,$ and the standard deviation for female consumers is assumed to be $$14.$ 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.

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