An airline wants to select a computer software package for i

An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps as few passengers as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is obtained, which gives rise to the following Excel output:

ANOVA                                                                                                                                      

Source of Variation          SS            df     MS       F                P-value        F crit

Between Groups              212.4       3              8.304985    0.001474     3.238867     

Within Groups                 136.4               8.525                                               

Total                                 348.8                                                                                                   

a) What is the within groups degrees of freedom for this analysis? Explain how you obtain your answer.

b) What is the total degrees of freedom? Explain how you obtain your answer.

c) What is the among-group (between-group) mean squares? Explain how you obtain your answer.

d) At a significance level of 1%, what conclusion can you infer? Explain how you obtain your answer.

Solution

(a)

df_within = SS_within/MS_within = 136.4/8.525 = 16

(b)

df_total = df_within + df_between = 16 +3 = 19

(c)

MS_between = SS_between/df_between = 212.4/3 = 70.8

(d)

P-value(0.001474)<alpha(0.01) , we reject the null hypothesis. In other words we infer that there is a significant difference in the number of reservation of passengers by these 4 packages.