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 50 male consumers was $135.67, and the average expenditure in a sample survey of 36 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $33, and the standard deviation for female consumers is assumed to be $22. 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)? At 99% confidence, what is the margin of error (to 2 decimals)? Develop a 99% confidence interval for the difference between the two population means (to 2 decimals). Use z-table. ( , )

Answer 1

The point estimate is $135.67 - $ 68.64 = $ 67.03

At 99% , the margin of error

Using Z-tables, the critical value is, Z (0.01/2) = Z(0.005) = +- 2.576

Margin of error, E = Z x sqrt((1/N1) + (1/N2))

N1 = Sample size of male consumers = 50

N2 = Sample size of female consumers = 36

Hence, E = 2.576 x sqrt ((1/50) + (1/36)) = 0.563 = 0.56

Develop a 99% confidence interval for the difference between the 2 population means = (Xbar1 – Xbar2) +or – E

= 67.03 + or – 0.56

= 67.59 , 66.47