Question

This information is for problems 7 – 14:
Two economics professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results:
                                                Mean Grade                      Standard Deviation
Professor Welker            83.6                                                        21.6
Professor Ackerman       79.7                                                        12.0
At the 0.01 level of significance, what is your conclusion?

	a.	Reject the null hypothesis and conclude the variances are different.
	b.	Fail to reject the null hypothesis and conclude the variances are different.
	c.	Reject the null hypothesis and conclude the variances are the same.
	d.	Fail to reject the null hypothesis and conclude the variances are the same.
	e.	Determine the test results are inconclusive.

This information is for problems 7 – 14:
Two economics professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results:
                                                Mean Grade                      Standard Deviation
Professor Welker            83.6                                                        21.6
Professor Ackerman       79.7                                                        12.0
At the 0.05 level of significance, what is your conclusion?

	a.	Reject the null hypothesis and conclude the variances are different.
	b.	Fail to reject the null hypothesis and conclude the variances are different.
	c.	Reject the null hypothesis and conclude the variances are the same.
	d.	Fail to reject the null hypothesis and conclude the variances are the same.
	e.	Determine the test results are inconclusive.

Answer 1

Let us take the cases of hypothesis

If null hypothesis then H0:

If alternate hypothesis then Ha:  

Variance of sample A(professor welker) is given as

Variance of sample B (Professor acerman) is given as

Sample Size for both is given as =10

So n1 and n2 will be 10

Estimated population variance of sample A is given as

In similar manner Estimated population variance of sample B is given as

F ratio is ratio of estimated population variance of both

at

Here the degree of freedom =(n1-1),(n2-1)=(10-1),(10-1)=9,9

Value of F from table will be 5.12

Calculated value of F is less than table value of T=5.12

So null hypothesis is accepted

D option will be Correct option

Fail to reject the null hypothesis and variance are same