Question

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 43 male consumers was $135.67, and the average expenditure in a sample survey of 36 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $39, and the standard deviation for female consumers is assumed to be $22. 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)? At 99% confidence, what is the margin of error (to 2 decimals)? 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. = 39)
μ₂ : Mean of population 2 (Std. dev. = 22)
μ₁ - μ₂ : Difference between two means

99% confidence interval results:

Difference	n1	n2	Sample mean	Std. err.	L. limit	U. limit
μ1 - μ2	43	36	67.03	6.9868832	49.032981	85.027019

Hence,

Point estimate = 67.03

Margin of error = (85.3342 - 48.7258)/2 = 18.30

99% confidence interval:

(48.73, 85.33)