MS5312 Business Statistics-Inferences about Population Variances

MS5312 Business Statistics-Inferences about Population Variances

Home Exercises

Question 1
Using a sample of 9 days over the past 6 months, a dentist has seen the following numbers of patients: 22, 25, 20, 18, 15, 22, 24, 19, and 26.
If the number of patients seen per day is normally distributed, would an analysis of these sample data reject the hypothesis that the variance in the number of patients seen per day is equal to 10? Use α = .10 level of significance. What is your conclusion?

Question 2
A research hypothesis is that the variance of stopping distances of automobiles on web pavement is substantially greater than the variance of stopping distances of automobiles on dry pavement. In the research study, 16 automobiles traveling at the same speeds are tested for stopping distances on wet pavement and then tested for stopping distances on dry pavement. On wet pavement, the standard deviation of stopping distances is 32 feet. On dry pavement, the standard deviation is 16 feet.

At a .05 level of significance, do the sample data justify the conclusion that the variance in stopping distances on wet pavement is greater than the variance in stopping distances on dry pavement?

Question 3
A manufacturer of hard safety hats for construction workers is concerned about the variation of the forces its helmets transmit to wearers when subjected to a standard external force. The manufacturer desires σ to be less than 40.
Tests were run on a random sample of n = 40 helmets, and the sample variance was found to be equal to 2350 pounds2. Do the data provide sufficient evidence to indicate that σ exceeds 40? (Hint: Use 40 degrees of freedom as an approximation.)

Question 4
The average useful life of a VCR is 6 years with a standard deviation of .75 years (Consumer Reports 1995 Buying Guide). A sample of the useful life of 30 television sets provided a sample standard deviation of 2 years.
Construct a hypothesis test that can be used to determine whether the standard deviation of the useful life of television sets is significantly greater than the standard deviation of the useful life of VCRs. With a .05 level of significance, what is your conclusion?

Question 5
Each day the major stock markets have a group of leading gainers in price (stocks that go up the most). On one day the standard deviation in the percent change for a sample of 10 NASDAQ leading gainers was 15.8. On the same day, the standard deviation in the percent change for a sample of 10 NYSE leading gainers was 7.9 (USA Today, September 14, 2000).

Conduct a test for equal population variances to see whether it can be concluded that there is a difference in the volatility of the leading gainers on the two exchanges. Use α = .10. What is your conclusion?

港人支持89北京民運，已不再是七十年代初 受中國官方策動與認可的「認識祖國」活動，而是由民間自發、與祖國廣大人民認同的民間民主運動，它為在親中路線失落後的 本土學生運動重新找回了支點，也促使了本土公民運動中的 精英分子向本土的政治運動過渡，形成了今天香港立法會內的民主派。

然而，北京當局也是 自89年六四慘案之後，開展了長達二十年 拖延香港民主發展的過程，不單為了有效管治香港，也為了有效阻截香港的民主發展對中共政權造成衝擊，令本地民運發展充滿陰霾。

北京中央政府在回歸後的香港政制安排上重重設障，將一個僅得薄弱民主成份的 立法會及 行政長官產生辦法寫進《基本法》中，致有91年香港市民火燒《基本法》定稿的壯烈之舉。

雖然其後英方 為了西方的利益強行加快97過渡前的政制民主化，而民主派人士也加快整合成民主黨，但本地民主人士已經開始軟弱下來，對為人民爭取最大的民主空間 和權利變得怯懦，致有95年 立法局全面直選的議案，因民主派議員一票之微的退縮 而功敗垂成的敗案！

而97年7月1日午夜的鐘聲一響，回歸前最後一屆，也是香港有史以來最民主化的立法局隨即解散，由一個中共欽點 且全權控制的臨時立法會取而代之，並將自92至97香港政制民主化的 立法成果全部取消，還原多條惡法，重新收縮香港的公民空間 (Public or Civic Space) 至80年代的水平。