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 41 male consumers was $135.67, and the average expenditure in a sample survey of 39 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $34, and the standard deviation for female consumers is assumed to be $22.

a. 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)?

b. 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)?

C. Develop a 99% confidence interval for the difference between the two population means (to 2 decimals).

Answer 1

a)

Point estimate = 135.67 - 68.64 = 67.03

b)

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(1156/41 + 484/39)
sp = 6.3722

Given CI level is 0.99, hence α = 1 - 0.99 = 0.01                  
α/2 = 0.01/2 = 0.005, zc = z(α/2, df) = 2.576                  
                  
Margin of Error                  
ME = zc * sp                  
ME = 2.576 * 6.3722                  
ME = 16.41

c)

                  
                  
CI = (x1bar - x2bar - tc * sp , x1bar - x2bar + tc * sp)                  
CI = (135.67 - 68.64 - 2.576 * 6.3722 , 135.67 - 68.64 - 2.576 * 6.3722                  
CI = (50.62 , 83.44)  

## if you take z value upto 2 decimal i.e.2.58answer would be change