Question

You are gearing up to open a new wine shop. In an effort to optimize wine sales, you collect data by observing your competition and noting what people are ordering during happy hour. Below is data collected during a 2 week period.

Cabernet Sauvignon	Merlot	Chardonnay
9	3	1
8	9	6
5	5	2
8	8	5
4	6	3
8	7	2
6	12	5
1	9	4
0	8	6
3	3	4
4	11	2
5	8	0
7	9	3
2	7	2

Explain why we need to do a one-way ANOVA test with this data. Perform a one-way ANOVA test at a 5% level of significance with F*= 4.08 Explain the decision we make and Build 95% confidence interval for each type of wine. Explain what this means.

Answer 1

Individual 95% CIs For Mean Based on
                         Pooled StDev
Level   N   Mean StDev   -+---------+---------+---------+--------
C1     14 5.000 2.828            (------*------)
C2     14 7.500 2.624                         (-----*------)
C3     14 3.214 1.847   (------*------)
                          -+---------+---------+---------+--------
                         2.0       4.0       6.0       8.0

Pooled StDev = 2.470

One-way ANOVA: C1, C2, C3

Source DF      SS     MS      F      P
Factor   2 129.76 64.88 10.64 0.000
Error   39 237.86   6.10
Total   41 367.62

S = 2.470   R-Sq = 35.30%   R-Sq(adj) = 31.98%

                         Individual 95% CIs For Mean Based on
                         Pooled StDev
Level   N   Mean StDev   -+---------+---------+---------+--------
C1     14 5.000 2.828            (------*------)
C2     14 7.500 2.624                         (-----*------)
C3     14 3.214 1.847   (------*------)
                          -+---------+---------+---------+--------
                         2.0       4.0       6.0       8.0

Pooled StDev = 2.470

Grouping Information Using Tukey Method

     N   Mean Grouping
C2 14 7.500 A
C1 14 5.000    B
C3 14 3.214    B

Means that do not share a letter are significantly different.

Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons

Individual confidence level = 98.06%

C1 subtracted from:

     Lower Center Upper ---------+---------+---------+---------+
C2   0.223   2.500 4.777                      (-----*------)
C3 -4.063 -1.786 0.491         (------*-----)
                           ---------+---------+---------+---------+
                                 -3.5       0.0       3.5       7.0

C2 subtracted from:

     Lower Center   Upper ---------+---------+---------+---------+
C3 -6.563 -4.286 -2.009 (------*-----)
                            ---------+---------+---------+---------+
                                  -3.5       0.0       3.5       7.0