A consumer group would like to compare the satisfaction ratings of three restaur

Question

A consumer group would like to compare the satisfaction ratings of three restaurant chains, A, B, and C. A random of satisfaction scores on a scale of 1-20 was collected from customers at each restaurant. The accompanying table contains the scores. a. Perform a one-way ANOVA using ?=0.05 to determine if there is a difference in the average satisfaction scores these three restaurants b. Perform a multiple comparison test to determine which pairs are different using ?= 0.05 ?Click the icon to view the data table Squares Freedom Squares F Source Between Within Total

Explanation / Answer

Answer:

a) The R-code for ANOVA is as;

y=c(15,17,16,18,17,15,10,12,14,11,13,16,17,19,15,14,15,16)
x=rep(c("a","b","c"),c(5,7,6))
d=data.frame(y,x);d
a=aov(y~x)
summary(a)

And the output is ;

> summary(a)
Df Sum Sq Mean Sq F value Pr(>F)
x 2 46.8 23.40 7.134 0.00665 **
Residuals 15 49.2 3.28
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Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Here p-value is less than 0.05 thus we reject H0 and conclude that there is significant difference in average scores of three restaurants.

b) For multiple comparison the R-code ia as follosw;

y=c(15,17,16,18,17,15,10,12,14,11,13,16,17,19,15,14,15,16)
x=rep(c("a","b","c"),c(5,7,6))
d=data.frame(y,x);d
a=aov(y~x)
TukeyHSD(a)

And the output is ;

> TukeyHSD(a)
Tukey multiple comparisons of means
95% family-wise confidence level

Fit: aov(formula = y ~ x)

$x
diff lwr upr p adj
b-a -3.6 -6.3545084 -0.8454916 0.0105074
c-a -0.6 -3.4485459 2.2485459 0.8494810
c-b 3.0 0.3828143 5.6171857 0.0240324

From above output the treatment B is significant. since the first and last difference having p-value is less than 0.05.

Thus the B is significant from A and C.

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