Question

The data of the samples taken from two piles are as follows.

	Yığın-1	Yığın-2
Sample Volume	12	9
Sample Average	34,56	41,73
Sample Variance	4,02	3,21

5% significance level,
a) Is there evidence that the 2nd stack variance is less than 3.1?
b) Is there evidence that the two stack variances are not equal?
c) Is there evidence that the average of the first stack is smaller than the average of the second stack? What is the p-value?

Answer 1

a). It is given that for second stack, we have

Testing for evidence that the nd stack variance is less than 3.1.

Level of significance:

Test statistic:

Critical region :

Now

Decision: Since the calculated value of does not fall in region of rejection, we fail to reject the null hypothesis.

Hence we conclude that there is not enough evidence to claim that the population variance is less than 3.1, at the .05 significance level.

b). Is there evidence that the two stack variances are not equal?

Level of significance:

Test Statistic:

Critical region     

Since the calculated value of F doesn't fall in the region of rejection, we fail to reject the null hypothesis.

Hence we conclude that there is not enough evidence that the two stack variances are not equal.

c) Is there evidence that the average of the first stack is smaller than the average of the second stack? What is the p-value?

Level of significance:

Test statistic: we shall be using a two sample independent t-test for testing in this case.

where is the pooled variance

The critical region is  

Since the calculated value of t falls in the rejection region, we reject the null hypothesis. Hence, we conclude that there is enough evidence to claim that population mean of first stack ​ is less than the second stack at the .05 significance level.

The p-value is 0.0000.