Question

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 $

Answer 1

x1            =	138.67	x2            =	61.64
n1           =	40	n2           =	30
σ1           =	35.00	σ2           =	20.00

a)

Point estimate of differnce '=x1-x2 =

77.03

b)

std error σ1-2=√(σ21/n1+σ22/n2)    =

6.630

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)