A new operator was recently assigned to a crew of workers wh

A new operator was recently assigned to a crew of workers who perform a certain job. From the records of the number of units of work completed by each worker each day last month, a sample of size five was randomly selected for each of the two experienced workers and the new worker. At the ? = .05 level of significance, does the evidence provide sufficient reason to reject the claim that there is no difference in the amount of work done by the three workers?

(a) Find the test statistic. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer bounds exactly.)
? < p < ?
(b) State the appropriate conclusion.

Reject the null hypothesis, there is not significant evidence of a difference in units of work between the workers.

Reject the null hypothesis, there is significant evidence of a difference in units of work between the workers.    

Fail to reject the null hypothesis, there is significant evidence of a difference in units of work between the workers.

Fail to reject the null hypothesis, there is not significant evidence of a difference in units of work between the workers.

	Workers
	New	A	B
Units of work (replicates)	9	13	9
	11	13	9
	11	13	11
	9	13	11
	10	12	9

Solution

One factor ANOVA

Mean

n

Std. Dev

10.0

5

1.00

New

12.8

5

0.45

A

9.8

5

1.10

B

10.9

15

1.64

Total

ANOVA table

Source

SS

   df

MS

F

   p-value

Treatment

28.13

2

14.067

17.58

.0003

Error

9.60

12

0.800

Total

37.73

14

F= 17.58

(ii) Find the p-value. (Give your answer bounds exactly.)

P=0.0003
0.001 < p < 0.0001

(b) State the appropriate conclusion.

Reject the null hypothesis, there is not significant evidence of a difference in units of work between the workers.

Reject the null hypothesis, there is significant evidence of a difference in units of work between the workers.    

Fail to reject the null hypothesis, there is significant evidence of a difference in units of work between the workers.

Fail to reject the null hypothesis, there is not significant evidence of a difference in units of work between the workers.

One factor ANOVA
	Mean	n	Std. Dev
	10.0	5	1.00	New
	12.8	5	0.45	A
	9.8	5	1.10	B
	10.9	15	1.64	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	28.13	2	14.067	17.58	.0003
Error	9.60	12	0.800
Total	37.73	14