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

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 48 male consumers was $135.67, and the average expenditure in a sample survey of 33 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $39, and the standard deviation for female consumers is assumed to be $24.

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

point estaimte of the difference : 135.67 - 68.64 = 67.03

alpha / 2 = 0.005   Z = 2.57

margin of error : 2.57 * srqt ( 39^2 / 48 + 24^2 / 33 ) = 18.016

I: 67.03 +/- 18.016

19.014 < miu1 - miu2 < 85.046

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