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 maleconsumers was $136.67, and the average expenditure in a sample survey of 30 female consumers was $66.64. 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

Given that,

For male :

For female :

a) The point estimate (in dollars) of the difference between the population mean expenditure for males and the population mean expenditure for females is,

=> Point estimate = $ 70.03

b) A 99% confidence level has significance level of 0.01and critical value is,

Margin of error ( E ) is,

Margin of error ( E ) = $20.60

c) The 99% confidence interval for the difference between the two population means is,

The 99% confidence interval is from $49.43 to $90.63