MS5312 Business Statistics-Analysis of Variance

MS5312 Business Statistics
Analysis of Variance
Exercises

Question 1
Which of the following components in an ANOVA table are not additive?
a) sum of squares
b) degrees of freedom
c) mean squares
d) It is not possible to tell.

Question 2
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, on average, 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 A C E 0.001474 3.238867
Within Groups 136.4 B D

Total 348.8

1) What are the values of A-E?
2) Referring to above ANOVA table, at a significance level of 1%, which of the following answer is correct?
a) there is insufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are not all the same.
b) there is insufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are all the same.
c) there is sufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are not all the same.
d) there is sufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are all the same.

Question 3
The computer Anxiety Rating Scale (CARS) measures an individual’s level of computer anxiety on a scale from 20 (no anxiety) to 100 (highest level of anxiety). Researchers at Miami University administered CARS to 172 business students. One of the objectives of the study was to determine if there are differences in the amount of computer anxiety experienced by students with different majors.

Source Degrees of Freedom Sum of Squares Mean Squares F
Among Majors 5 3,172
Within Majors 166 21,246
Total 171 24,418

Major n Mean
Marketing 19 44.37
Management 11 43.18
Other 14 42.21
Finance 45 41.80
Accountancy 36 37.56
MIS 47 42.21
Source: Travis Broome, and Douglas Havelka, “Determinants of computer anxiety in business students,” The Review of Business Information Systems, Spring 2002, 6(2): 9-16.

a. Complete the ANOVA summary table.
b. At the 0.05 level of significance, is there evidence of a difference in the average computer anxiety experienced by different majors?


Question 4
Three universities administer the same comprehensive examination to the recipients of MS degrees in psychology. From each institution, a random sample of MS recipients was selected, and these recipients were then given the exam. The following table shows the scores of the students from each university.

University A University B University C
89 60 81
95 95 70
75 89 90
92 80 78
99 66
77
Sample mean 90 81 77

1) Calculate SSA, SSW, and F values. (hand calculation) (Note that the sample sizes are not equal.)
2) Do this test using Excel and compare whether (1) and (2) get the same results.

三、回歸祖國 民主倒退

中央政府這種推倒重來的策略，再加上它在《基本法》中設限，令回歸後的香港社會猶如孫行者戴了金剛箍，在緊箍咒下動彈不得，公民空間大受拘禁。中央政府只集中統戰香港的權貴商家，《基本法》內訂明的政制無不偏袒他們，令裙帶資本主義得以維持。

在這政經脈絡下，產生了小圈子的特首選舉、功能組別佔立法會一半總數、分組點票、行政主導等不義的制度。

九七後的香港，彷彿仍然處於殖民地時代，只是換了主子而已。

決策權力仍然高度集中在 非民選的特區政府行政部門之內。民選議員不單權力有限，其議席也只佔立法會的一半，而這個局部民選的立法會的政策制訂能力，更受到分組點票及有限提案權的掣肘；在分組點票制度下，立法會不過是橡皮圖章。

此外，英人遺下的諮詢架構，也在長官意志 愈演愈烈的情況下逐漸失效，令民意更難影響政府施政，遂令香港市民對特區政府、立法會以及各政黨，日漸產生失望的情緒。顯而易見，期盼在不公義的建制內爭取民主，或希望專權的政府落實香港民主，是不切實際的幻想。

回歸十多年，香港人擁有的自由 不斷受到侵蝕，《基本法》二十三條立法、七一後名嘴封咪、取締民間電台以及廣管局干預港台編輯自主的方針，令這些公民自由受到嚴厲的挑戰。現時香港社會真正獨立的媒體少之又少，而大氣電波卻遲遲未開放。

同時，香港社會發生了一連串重要事件，為香港這個特殊城市的新殖民地歷史，烙下了特殊的印記，其中最重要的，肯定是03及04年7月1日 超過五十萬人上街的日子， 06年底及07年 中本土青年人發起反對拆除天星及皇后碼頭的行動，並因灣仔利東街的清拆 引發就市區重建的抗爭，

與及09年六四廿週年 破紀錄的二十萬人參與維園燭光悼念會等等，這在在反映民間公民社會的潛在力量仍然強大。過去幾年，對市區收樓重建、新界收地基建、政府賤賣領滙、古蹟拆卸的反對運動延綿不斷，一群群在議會建制外的民主及公民運動鬥士已經形成且愈趨成熟。

這也預示了回歸後的香港社會，開始「兩條腿走路」： 已經進入主流或 官方認可的政治架構的公民運動人士，即現今立法會內的泛民主派，要在議會內與北京當局操控的特區政府及 議會內的大小保皇集團進行抗爭，令其少做官商勾結和中外資本勢力勾結的壞事；

而另一方面，議會外仍有大量民間人士 在各個層面努力工作，一方面喚醒香港市民 關注自己的切身權益是否受損受制，另方面也以非黨派的中立角色努力開拓與擴闊公民空間。