Question

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 q table.) Restaurant Inspector 72 68 73 69 75 84 85 80 82 84 54 59 60 56 xc 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.) Answer is complete and correct. ANOVA Source of Variation Rows Columns Error Total df MS p-value 8.9330 1,723.6000 67.0670 1,799.6000 2.2330 0.8920 0.0000 0.266 28618000 102.799 8.3830 14 a-2. At the 5% significance level, can you conclude that the average grades differ by restaurant? Yes, since the p-value associated with restaurant is less than significance level. OYes, since the p-value associated with restaurant is greater than significance level. No, since the p-value associated with restaurant is less than significance level. No, since the p-value associated with restaurant is greater than significance level. b. If the average grades differ by restaurant, use Tukey's HSD method at the 5% significance level to determine which averages differ (If the exact value for n is not found in the table, use the average of corresponding upper& lower studentized range values. Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Answer is not complete Population Mean Differences Does The Average Differ? Confidence Interval 8.18

Answer 1

column data , i (Factor B)	1	2	3
count, ni =	5	5	5
mean , x̅ i =Σxi / ni	71.400	56.800	83.000

Level of significance	0.05
no of treatments	3
df error	8
MSE	8.383
q-statistic value	4.043

critical value = q*√(MSE/n) = 5.2351

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	14.6	5.2351	9.36	19.84	yes,means are different
µ1-µ3	-11.6	5.2351	-16.84	-6.36	yes,means are different
µ2-µ3	-26.2	5.2351	-31.44	-20.96	yes,means are different