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 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 $35, and the standard deviation for female consumers is assumed to be $20.
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.
The solution gives detailed steps on calculating point esitimate of mean differences, margin of error and confidence intervals under given confidence level if the mean and standard deviation for each of two groups are given.