Question

The USA Today 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 47 male consumers was $135.67, and the average expenditure in a sample survey of 35 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $40, and the standard deviation for female consumers is assumed to be $16.

a.) What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females (to 2 decimals)?

b.) At 99% confidence, what is the margin of error (to 2 decimals)?

c.) Develop a 99% confidence interval for the difference between the two population means (to 2 decimals).

Answer 1

Part a)

Part b)

Margin of Error =    = 16.57

Part c)

Confidence interval :-

Z(α/2) = Z (0.01 /2) = 2.576 ( Critical value from Z table )

Lower Limit =
Lower Limit = 50.46
Upper Limit =
Upper Limit = 83.60
99% Confidence interval is ( 50.46 , 83.60 )