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 $137.67, and the average expenditure in a sample survey of 30 female consumers was $65.64. Based on past surveys, the standard deviation for male consumers is assumed to be $45, 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

Part a)

Point Estimate =   =  ( 137.67 - 65.64 ) = 72.03

Part b)

Margin of Error =

Confidence interval :-

Z(α/2) = Z (0.01 /2) = 2.576

Lower Limit =
Lower Limit = 51.43
Upper Limit =
Upper Limit = 92.63
99% Confidence interval is ( 51.43 , 92.63 )