Question

THIS IS THE THIRD TIME ASKING THE SAME QUESTION, PLEASE DOUBLE CHECK YOUR ANSWERS. THANK YOU. AND ANSWER ALL PARTS A, B AND C

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 44 male consumers was $135.67, and the average expenditure in a sample survey of 32 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $36, and the standard deviation for female consumers is assumed to be $20.

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). Use z-table. ( , )

Answer 1

n1 = 44

= 135.67

= 36

n2 = 32

= 68.64

= 20

Claim: Male and female consumers differ in the amounts they spend.

The null and alternative hypothesis is

a)

The point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females is

= 135.67 - 68.64 = 67.03

b)

Here E is the margin of error.

Zc = 2.58

( From z table)

c)

We have to find a 99% confidence interval for the difference in population mean.

Formula is

67.03 - 16.71 < < 67.03 + 16.71

50.32 < < 83.74

Confidence interval: ( 50.32 , 83.74)

---------------------------------------------------------------------------------------------------------------------

The value zero (0) is not belongs to confidence interval we reject null hypothesis.

Conclusion: Male and female consumers differ in the amounts they spend.

---------------------------------------------------------------------------------------------------------

If you have any doubt please comment!