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Question Workspace Check My Work (2 remaining) The USA Today reports that the average expenditure on...

Question Workspace Check My Work (2 remaining) The USA Today reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 40 male consumers was $135.67, and the average expenditure in a sample survey of 30 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $38, and the standard deviation for female consumers is assumed to be $19.

A. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females (to 2 decimals)?

B. At 99% confidence, what is the margin of error (to 2 decimals)?

C. Develop a 99% confidence interval for the difference between the two population means (to 2 decimals). Use z-table. ( __,__ )

Homework Answers

Answer #1

The statistical software output for this problem is:

Two sample Z summary confidence interval:
μ1 : Mean of population 1 (Std. dev. = 38)
μ2 : Mean of population 2 (Std. dev. = 19)
μ1 - μ2 : Difference between two means

99% confidence interval results:

Difference n1 n2 Sample mean Std. err. L. limit U. limit
μ1 - μ2 40 30 67.03 6.9378191 49.159362 84.900638

Hence,

a) Point estimate = 67.03

b) Margin of error = (84.90 - 49.16)/2 = 17.87

c) 99% confidence interval:

(49.16, 84.90)

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