Question

1) The Zino restaurant chain is conducting an analysis of its restaurants, which take pride in serving burgers and fries to go faster than the competition. As a part of its analysis, Zino wants to determine if its speed of service is different across its four outlets. Orders at Zino restaurants are tracked electronically, and the chain is able to determine the speed with which every order is filled. The chain decided to randomly sample 20 orders from each of the four restaurants it operates. The speed of service for each randomly sampled order was noted and is contained in the excel file Zino.

a. At the alpha = 0.05 level of service, can Zino conclude that the speed of service is different across the four restaurants in the chain?

b. If the chain concludes that there is a difference in speed of service, is there a particular restaurant the chain should focus its attention on? Use the Tukey-Kramer multiple comparisons procedure to support your decision. Use alpha = 0.05.

Restaurant 1	Restaurant 2	Restaurant 3	Restaurant 4
260	205	275	248
246	236	251	244
263	233	253	259
249	220	272	257
230	234	255	252
240	230	253	233
238	223	256	235
254	241	229	269
242	226	263	251
230	211	264	268
257	239	265	270
254	190	241	259
215	242	267	236
229	231	261	250
243	215	249	237
248	221	264	269
244	225	240	262
233	222	231	243
246	242	262	270
254	214	243	245

Answer 1

a.

One-way ANOVA: Speed of Service versus Restaurant

Source DF SS MS F P
Restaurant 3 11077 3692 22.67 0.000
Error 76 12381 163
Total 79 23458

Since p-value<0.05 Zino can conclude that the speed of service is different across the four restaurants in the chain.

b.

Grouping Information Using Tukey Method

C1 N Mean Grouping
Restaurant 3 20 254.70 A
Restaurant 4 20 252.85 A B
Restaurant 1 20 243.75 B
Restaurant 2 20 225.00 C

Means that do not share a letter are significantly different.

Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of C1

Individual confidence level = 98.97%

C1 = Restaurant 1 subtracted from:

C1 Lower Center Upper ------+---------+---------+---------+---
Restaurant 2 -29.37 -18.75 -8.13 (----*---)
Restaurant 3 0.33 10.95 21.57 (---*----)
Restaurant 4 -1.52 9.10 19.72 (----*---)
------+---------+---------+---------+---
-25 0 25 50

From the above confidence intervals, we see that confidence interval of Restaurant 2-Restaurant 1 contains only negative numbers and confidence interval of Restaurant 3-Restaurant 1 contains only positive numbers and confidence interval of Restaurant 4 -Restaurant 1 contains zero hence we conclude that the speed of service of Restaurant 3> the speed of service of Restaurant 1 and the speed of service of Restaurant 1> the speed of service of Restaurant 2 and there is insignificant difference in the speed of service in Restaurants 1 and 4.
C1 = Restaurant 2 subtracted from:

C1 Lower Center Upper ------+---------+---------+---------+---
Restaurant 3 19.08 29.70 40.32 (---*---)
Restaurant 4 17.23 27.85 38.47 (---*---)
------+---------+---------+---------+---
-25 0 25 50

From the above confidence intervals, we see that confidence interval of Restaurant 3-Restaurant 2 contains only positive numbers and confidence interval of Restaurant 4-Restaurant 2 contains only positive numbers hence we conclude that the speed of service of Restaurant 3> the speed of service of Restaurant 2 and the speed of service of Restaurant 4> the speed of service of Restaurant 2.
C1 = Restaurant 3 subtracted from:

C1 Lower Center Upper ------+---------+---------+---------+---
Restaurant 4 -12.47 -1.85 8.77 (---*----)
------+---------+---------+---------+---
-25 0 25 50

From the above confidence interval, we see that confidence interval of Restaurant 4 -Restaurant 3 contains zero hence we conclude that there is insignificant difference in the speed of service in Restaurants 3 and 4.

From above discussion, we see that the speed of service in Restaurants 1, 3 and 4>the speed of service in Restaurant 2.

So we conclude that there is a particular restaurant i.e. Restaurant 2 the chain should focus its attention on.