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 48 male consumers was $135.67, and the average expenditure in a sample survey of 34 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $40, and the standard deviation for female consumers is assumed to be $23.

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

a)

point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females = 135.67 - 68.64 = 67.03

b)

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(1600/48 + 529/34)
sp = 6.9923

Given CI level is 0.99, hence α = 1 - 0.99 = 0.01              
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 2.58          
              
Margin of Error              
ME = tc * sp              
ME = 2.58 * 6.9923              
ME = 18.04

c)

              
CI = (x1bar - x2bar - tc * sp , x1bar - x2bar + tc * sp)                  
CI = (135.67 - 68.64 - 2.58 * 6.9923 , 135.67 - 68.64 - 2.58 * 6.9923                  
CI = (48.99 , 85.07)