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 40 male consumers was $135.67, and the average expenditure in a sample survey of 30 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 $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.

Explanation / Answer

Ans:

a)

Point estimate=(135.67-68.64)=67.03

b) z value(two tailed) for 99% confidence level is 2.58

standard error=sqrt(35^2/40)+(20^2/30))=6.63

Margin of error=2.58*6.63=17.11

c)99% confidence interval

=67.03+/-17.11

=(49.92,84.14)

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