MS5312 Business Statistics-Inferences about Population Variances

MS5312 Business Statistics
Inferences about Population Variances
Exercises

Question 1
The manufacturer of a machine to package soap powder claimed that her machine could load cartons at a given weight with a range of no more than 0.4 ounce. The mean and variance of a sample of eight 3-pound boxes were found to equal 3.1 and 0.018, respectively.

Test the hypothesis that the variance of the population of weight measurements is σ2  0.01 against the alternative that σ2 > 0.01. Use an α = 0.05 level of significance.
a. What assumptions are required for this test?
b. Test the hypothesis.


Question 2
An experiment published in The American Biology Teacher studied the efficacy of using 95% ethanol and 20% bleach as disinfectants for removing bacterial and fungal contamination when culturing plant tissues. The experiment was repeated 15 times with each disinfectant, using eggplant as the plant tissue cultured.

Relevant data is given in the following table. Are you willing to assume that the underlying population variances are equal? Use α = 0.05.

Disinfectant 95% Ethanol 20% Bleach
Mean 3.73 4.80
Variance 2.78095 0.17143
n 15 15


Question 3
Suppose that we wish to compare the variation in diameters of parts produced by our company with the variation in diameters of parts produced by a competitor. The sample variance for our company, based on n = 10 diameters, was S12 = 0.0003.
In contrast, the sample variance of the diameter measurements for 20 of the competitor’s parts was S22 = 0.0001.

Do the data provide sufficient information to indicate a smaller variation in diameters for the competitor? Test with α = 0.05.

Question 4
Aptitude tests should produce scores with a large amount of variation so that an administrator can distinguish persons with low aptitude and persons with high aptitude. The standard test used by a certain industry has been producing scores with a standard deviation of 10 points.

A new test is given to 20 prospective employees and produces a sample standard deviation of 12 points. Are scores from the new test significantly more variable than scores from the standard?
Use α = 0.01.

把政制發展的決定權還給人民！

五區總辭 全民公決 爭取2012年雙普選

一、前言

香港民主運動舉步維艱，主因之一是缺乏民眾的廣泛參與。民眾未有廣泛參與的因素很多：多年的殖民地教育和殖民地封閉體制固然是原因，而中央一再設限，且得到香港既得利益階層的呼應，更令香港市民有很高的政治無能感，但一個更重要的原因是：

本地民主運動 往往停留在 表面的代理層次，未能令民眾 透過親身參與來實踐理念、進行反思，令他們明白群眾的力量，可以改變政府政策 及改善自己的生活，從而認同民主的好處，以至在七一大遊行的 激情過後，民主運動便無以為繼。

如今，我們面臨一個非常重要的歷史關口，因為曾蔭權的特區政府在拖延了足足一年之後，終於要為2012政制發展的中途方案進行社會諮詢。

然而，頹敗至亟復甘願當奴的特首，已經發話，這方案將完全與 2017及2020年的 普選無關。擺在我們面前的是一個完全無助於 港人達到最終雙普選的政制爛方案，我們已無可選擇要進行抗爭。

二十年來，民主派用盡所有方法爭取民主，較重要的包括維園八八直選集會，《基本法》草擬期間及八九民運之後，多次提出 增加民主成份的政制方案，2003年 2004年兩次50萬人 上街爭取還政於民，以至 2005年12月的爭取普選大遊行。

然而，過往爭取民主的方法都效果不彰，民主進程裹足不前，民主派需要考慮提出進一步的有效行動，「五區總辭，全民公決」是目前最可行的出路。