Question

6 Given a recent outbreak of illness caused by E. coli bacteria, the mayor in a large city is concerned that some of his restaurant inspectors are not consistent with their evaluations of a restaurant's cleanliness. In order to investigate this possibility, the mayor has five restaurant inspectors grade (scale of O to 100) the cleanliness of three restaurants. The results are shown in the accompanying table. (You may find it useful to reference the g table.) 12.5 Restaurant Inspector 69 71 72 67 75 57 82 85 78 81 87 61 54 Hint Print a-1. Construct an ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "SS"', "MS', "p-value" to 4 decimal places and "P" to 3 decimal places.) ANOVA Source of Variation Rows Columns Error Total df MS p-value 0.0000

Answer 1

a)

using excel data analysis tool for two way anova,o/p is

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
1	3	208	69.333	156.333
2	3	214	71.333	182.333
3	3	205	68.333	142.333
4	3	209	69.667	105.333
5	3	216	72	279
1	5	354	70.8	9.2
2	5	285	57	7.5
3	5	413	82.6	12.3
ANOVA
Source of Variation	SS	df	MS	F	P-value
Rows	27.0667	4	6.7667	0.609	0.6679
Columns	1641.7333	2	820.8667	73.841	0.0000
Error	88.9333	8	11.1167
Total	1757.7333	14

b)

Level of significance	0.05
no of treatments	3
df error	8
MSE	11.1167
q-statistic value	4.043

column data ,	1	2	3
count, ni =	5	5	5
mean , x̅ i	70.800	57.000	82.600

critical value = q*√(MSE/2*(1/ni+1/nj))=6.0285

			confidence interval
population mean difference		critical value	lower limit	upper limit	result
µ1-µ2	13.8	6.0285	7.77	19.83	yes,means are different
µ1-µ3	-11.8	6.0285	-17.83	-5.77	yes,means are different
µ2-µ3	-25.6	6.0285	-31.63	-19.57	yes,means are different