The average expenditure on Valentine\'s Day was expected to be $100.89 (USA Toda

Question

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 42 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 $35, and the standard deviation for female consumers is assumed to be $21.

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. At 99% confidence, what is the margin of error (to 2 decimals)?

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

Explanation / Answer

given average expenditure =$100.89

sample survey of males n= 42

average expenditure = x^1=$135.67

standard deviation of males = $35

sample survey of females n= 36

average expenditure of females x^2 = $ 68.64

standard deviation of females = s= $21

a) The point estimate = average expenditure of males - average expenditure of females = x^1 -x^2

$135.67 - $68.64 = $67.03

b) 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 1/40 + 1/30= 0.62

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

(X-bar1 – X-bar2) ± E   

= 67.03 ± 0.62

= 66.41, 67.65

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