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 50 male consumers was $135, and the average expenditure in a sample survey of 31 female consumers was $66. 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 $16. 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. to

Explanation / Answer

A) point of estimate of difference between the population mean expenditure = 135 - 66 = 69

B) Margin of error = Z0.995 * sqrt (sd12/n1 + sd 22/ n 2)

= 2.576 * sqrt ((35)2 / 50 + (16)2/31)

= 14.74

C) cinfidence interval = Mean difference +/- margin of error

= 69 +/- 14.74

= 54.26, 83.74

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