Question

# You may need to use the appropriate appendix table or technology to answer this question. A...

You may need to use the appropriate appendix table or technology to answer this question.

A newspaper reports that the average expenditure on Valentine's Day is \$100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 40 male consumers was \$138.67, and the average expenditure in a sample survey of 30 female consumers was \$61.64. 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.

(a)

What is the point estimate (in dollars) of the difference between the population mean expenditure for males and the population mean expenditure for females? (Use male − female.)

\$

(b)

At 99% confidence, what is the margin of error (in dollars)? (Round your answer to the nearest cent.)

\$

(c)

Develop a 99% confidence interval (in dollars) for the difference between the two population means. (Use male − female. Round your answer to the nearest cent.)

\$  to \$

 x1            = 138.67 x2            = 61.64 n1           = 40 n2           = 30 σ1           = 35 σ2           = 20

a)

 Point estimate of differnce '=x1-x2 = 77.03

b)

 std error σ1-2=√(σ21/n1+σ22/n2)    = 6.63
 for 99 % CI value of z= 2.576 margin of error E=z*std error = 17.09

c)

 lower bound=(x1-x2)-E = 59.952 Upper bound=(x1-x2)+E = 94.108 from above 99% confidence interval for population mean =(59.95 to 94.11)