Question

he 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 47 male consumers was $135.67, and the average expenditure in a sample survey of 32 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $36, and the standard deviation for female consumers is assumed to be $18.

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

The statistical software output for this problem is:

Hence,

a) Point estimate = 67.01

b) Margin of error = (82.8456 - 51.2144)/2 = 15.82

c) 99% confidence interval:

(51.21, 82.85)