Question

A company wishes to purchase one of five different machines, A, B, C, D, E. The manager conducted the experiment to determine if performance of these machines is different. Test the hypothesis that the performance is different at 0.05 significance. Testing scores are in the table below.

A	68	72	77	42	53
B	72	53	63	53	48
C	60	82	64	75	72
D	48	61	57	64	50
E	64	65	70	68	53

Answer 1

Hypotheses are:

H0: Performance of these machines is same.

Ha: Performance of these machines is different.

Following is the output of one way ANOVA:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
A	5	312	62.4	210.3
B	5	289	57.8	92.7
C	5	353	70.6	76.8
D	5	280	56	47.5
E	5	320	64	43.5
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	658.16	4	164.54	1.747451147	0.17921408	2.866081402
Within Groups	1883.2	20	94.16
Total	2541.36	24

The F test statistics is:

F = 1.747

The p-value is: 0.1792

Since p-value is greater than so we fail to reject the null hypothesis.

That is we cannot conclude that  performance of these machines is different.