Question

USA Today reports that the average expenditure on Valentine's Day was expected to be $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 58 male consumers was 132.36, and the average expenditure in a sample survey of 32 female consumers was 60.36. Based on past surveys, the standard deviation for male consumers is assumed to be $30, and the standard deviation for female consumers is assumed to be $12. 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?

Answer 1

The point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females is the difference between the sample mean expenditure for males and the sample mean expenditure for females. That is:

point estimate = x¯m − x¯f = 132.36 − 60.36 = 72

Therefore, the point estimate is $72. This means that, based on the sample data, male consumers spend on average $72 more than female consumers on Valentine’s Day. However, this is only an estimate and not the exact difference. To construct a confidence interval for the true difference, we would need to use the formula for large, independent samples12.