Question

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 α = .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?

	Workers
	New	A	B
Units of work (replicates)	9	11	13
	8	10	11
	10	13	9
	8	13	11
	10	13	12

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


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

An experiment was designed to compare the lengths of time that four different drugs provided pain relief after surgery. The results (in hours) follow. Is there enough evidence to reject the null hypothesis that there is no significant difference in the length of pain relief provided by the four drugs at α = .05?

Drug
A	B	C	D
4	5	7	2
5	5	8	2
3	6	12	4
4	5	9
		10

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


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

Answer 1

Ans a ) using excel>data>data analysis >one way ANOVA

we have

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
New	5	45	9	1
A	5	60	12	2
B	5	56	11.2	2.2
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	24.13333	2	12.06667	6.961538	0.009839	3.885294
Within Groups	20.8	12	1.733333
Total	44.93333	14

(a) the test statistic F = 6.96

(ii)the p-value
0.005<p <0.01

Ans 2 )

using excel>data>data analysis >one way ANOVA

we have

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
A	4	16	4	0.666667
B	4	21	5.25	0.25
C	5	46	9.2	3.7
D	3	8	2.666667	1.333333
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	101.2208	3	33.74028	20.02721	5.78E-05	3.490295
Within Groups	20.21667	12	1.684722
Total	121.4375	15

(a) the test statistic F = 20.03

(ii)the p-value
0.<p <0.00001