The USA Today reports that the average expenditure on Valentine\'s Day is $100.8

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 48 male consumers was $135.67, and the average expenditure in a sample survey of 40 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $32, and the standard deviation for female consumers is assumed to be $19.

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)?

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

Develop a 99% confidence interval for the difference between the two population means (to 2 decimals). Use z-table.
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Explanation / Answer

Answer is as follows :

a) What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females?

The point estimate is (X) = (male average - female average)

i.e. 135.67 - 68.64 = 67.03

b) At 99% confidence, what is the margin of error ?

Using Z- table the critical value at 99 % confidence is

Z(0.01/2) = Z(0.005) = ± 2.576

So Margin error = Z 1/n1 + 1/n2 where n1 is no of males and n2 is no of females

So

2.576 *1/48 + 1/40 = 2.576 * 0.045 = 2.576 * 0.21 = 0.54

c) Develop a 99% confidence interval for the difference between the two population means

So now

X ± E i.e. 67.03 ±0.54

So the values are

67.03 + 0.54 = 67.57

67.03 - 0.54 = 66.49

if there is any query please ask in comments..

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