Question

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. ( __,__ )

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)