Question

The average expenditure on Valentine's Day was expected to be $100.89 (USA Today, February 13, 2006). Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 58 male consumers was $139, and the average expenditure in a sample survey of 33 female consumers was $61.31. Based on past surveys, the standard deviation for male consumers is assumed to be $33, and the standard deviation for female consumers is assumed to be $20. The z value is 2.576 . 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

Answer 1

Solution:

Given:

Sample 1 Male:

n₁ = 58

Sample 2 Female:

n₂ =33

z value for 99% confidence level = 2.576

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

the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females is given by:

Part b) At 99% confidence, what is the margin of error?

Formula:

Part c) Develop a 99% confidence interval for the difference between the two population means

Formula:

Thus we are 99% confident that  the difference between the population mean expenditure for males and the population mean expenditure for females is between: ( $63.37 to $92.01 )