Question

CH13 Q7

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.) 10 points Restaurant Inspector 73 68 72 72 72 53 58 62 59 56 86 eBook 80 85 Hint he 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 "F' to 3 decimal places.) ANOVA Source of Variation Rows Columns Error Total MS p-value 14.9330 3.7333 0.346 0.8397 0.0000 86.2667 10.7833 101.1997 13

Answer 1

using excel data analyis tool for two way anova woithout replication

a-1

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
Row 1	3	212	70.66666667	276.3333333
Row 2	3	208	69.33333333	145.3333333
Row 3	3	214	71.33333333	81.33333333
Row 4	3	216	72	169
Row 5	3	216	72	256
Column 1	5	357	71.4	3.8
Column 2	5	288	57.6	11.3
Column 3	5	421	84.2	10.2
ANOVA
Source of Variation	SS	df	MS	F	P-value
Rows	14.9333	4	3.7333	0.346	0.8397
Columns	1769.7333	2	884.8667	82.059	0.0000
Error	86.2667	8	10.7833
Total	1870.9333	14

b)

Level of significance	0.05
Numerator d.f.	3
Denominator d.f.	8
MSE	10.7833
q-statistic value	3.7728

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

confidence interval = mean difference ± critical value                  
                  
if confidence interval contans zero, then means are not different.                  

			confidence interval
population mean difference		critical value	lower limit	upper limit	result
µ1-µ2	13.800	5.9344	7.866	19.734	means are different
µ1-µ3	-12.800	5.9344	-18.734	-6.866	means are different
µ2-µ3	-26.600	8.3926	-34.993	-18.207	means are different