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 52 male consumers was $140, and the average expenditure in a sample survey of 38 female consumers was $62. 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 $10. 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.

Answer 1

a. As we want to check if male and female consumers differ in the amounts they spend.

So, the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females is

b. We have

The, the margin of error at 99% confidence is given by

c. The 99% confidence interval for the difference between the two population means is given by

Hence, the 99% confidence interval for the difference between the two population means is (65.4928,90.5072)