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 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 $39, and the standard deviation for female consumers is assumed to be $17.

1.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)?

2. At 99% confidence, what is the margin of error (to 2 decimals)?

3. Develop a 99% confidence interval for the difference between the two population means (to 2 decimals). Use z-table.

Answer 1

1. The point of estimation between the mean for males and females is 135.67 - 68.64 = 67.03

2. 99% confidence level, the margin of error = z(0.01/2) =z(0.005) =$\pm$2.576(using Z value)

Error E = Z Sqrt((1/n1)+(1/n2)) ((Squareroot - sqrt))

n1 = 40, n2 = 30

=2.576 * Sqrt((1/40)+(1/30))

=0.62

3. 99% confidence interval

67.03+0.62, 67.03-0.62

=67.65, 66.41