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. ge satisfaction scores i Satisfaction Scores for Three Restaurants Satisfaction Score A (1) 11 B (2) C (3) 14 17 s and conclude that the 12 18 16 10 17 18 13 15 19 values of the differences 14 13 12 16 14 12 Print Done Find the Tukey-Kramer critical range for each pair of samples. The critical range for samples 1 and 2 is CR12 (Round to two decimal places as needed.) 2.Find the Tukey-Kramer critical range CR1,3 for restaurants A and C, rounding to two decimal places 3.Find the Tukey-Kramer criitcal range CR2,4 for restaurants B and C, rounding to two decimal places 4.Compare the absolute values of the differences between the means of Tukey-Kramer critical ranges

Answer 1

Hypothesis :

H0 : μ1 = μ2 = μ3

Ha : atleast one μ is different

Treatment →	A	B	C
Input Data →	11.0 12.0 10.0 13.0 14.0	14.0 18.0 17.0 15.0 13.0 16.0 12.0	17.0 16.0 18.0 19.0 12.0 14.0

Treatment →	A	B	C	Pooled Total
observations N	5	7	6	18
sum ∑xi∑xi	60.0000	105.0000	96.0000	261.0000
mean ¯xx¯	12.0000	15.0000	16.0000	14.5000
sum of squares ∑x2i∑xi2	730.0000	1,603.0000	1,570.0000	3,903.0000
sample variance s2s2	2.5000	4.6667	6.8000	6.9706
sample std. dev. ss	1.5811	2.1602	2.6077	2.6402
std. dev. of mean SE¯xSEx¯	0.7071	0.8165	1.0646	0.6223

source	sum of squares SS	degrees of freedom νν	mean square MS	F statistic	p-value
treatment	46.5000	2	23.2500	4.8438	0.0238
error	72.0000	15	4.8000
total	118.5000	17

p value = 0.0238 < 0.05, So reject H0, Not all means are equal

post-hoc Tukey HSD Test Calculator results:

k=3 treatments
degrees of freedom for the error term ν=15
Critical values of the Studentized Range Q statistic:

At α=0.01,k=3,ν=15 Qcritical= 4.8341

At α=0.05,k=3,ν=15 Qcritical= 3.6719

Q1,2,3,4 Answers

Tukey HSD results

treatments pair	Tukey HSD Q statistic	Tukey HSD p-value	Tukey HSD inferfence
A vs B	3.3072	0.0807676	insignificant
A vs C	4.2640	0.0222569	* p<0.05
B vs C	1.1602	0.6859788	insignificant