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)?
   67.03
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

Let be the population mean expenditure for male consumers.

Let be the population mean expenditure for female consumers.

n1 = 48, n2 = 34

,

Here population standard deviations are known.

a) The point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females is

= 135.67 - 68.64

= 67.03

The point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females is 67.03

b)

Confidence level = c = 0.99

Margin of error (e) :

where zc is z critical value (1+c)/2 = (1+0.99)/2 = 0.995

zc = 2.58                (From statistical table of z values)

e = 2.58 * 6.9923            (Round to 4 decimal)

e = 18.04              (Round to 2 decimal)

Margin of error = 18.04

c) 99% confidence interval for the difference between the two population means is

                

99% confidence interval for the difference between the two population means is (48.99, 85.07)