Question

Check My Work eBook The average expenditure on Valentine's Day was expected to be $100.89 (USA Today, February 13, 2006). Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 46 male consumers was $139.52, and the average expenditure in a sample survey of 37 female consumers was $68.83. Based on past surveys, the standard deviation for male consumers is assumed to be $35, and the standard deviation for female consumers is assumed to be $20. The z value is 2.576. Round your answers to 2 decimal places. a. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females? b. At 99% confidence, what is the margin of error? c. Develop a 99% confidence interval for the difference between the two population means.

Answer 1

1. What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females?

Ans: The point estimate is $139.52 - $68.83 = $70.69.

2. At 99% confidence, what is the margin of error?

Ans: Using Z-tables, the critical value is

Z (0.01/2) = Z (0.005) = ± 2.576

Margin of error, E = Z √1/n1 + 1/n2

= 2.576 √1/46 + 1/37

= 2.576 √(0.022+.027)

=0.57

3. Develop a 99% confidence interval for the difference between the two population means.

Ans: (X-bar1 – X-bar2) ± E

70.69 ± 0.57

70.12 , 71.26