MS5312 Business Statistics-Inferences about Two Population Means

MS5312 Business Statistics

Inferences about Two Population Means

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Question 1
Independent random samples of n1 = 16 and n2 = 13 observations were selected from two normal populations with equal variances. The sample means and variances are shown in the accompanying table.

Find a 99% confidence interval for (1  2). Interpret this interval.

Population 1 Population 2
Sample size 16 13
Sample mean 34.6 32.2
Sample variance 4.8 5.9

Question 2
Repeat Question 3 of Exercises if your research objective is to show that 1 is different from 2.

Question 3
Figure Perfect, Inc., is a women’s figure salon that specializes in weight reduction programs. Weights for a sample of clients before and after a six-week introductory program follow.

Client Weight
Before After
1 140 132
2 160 158
3 210 195
4 148 152
5 190 180
6 170 164
Using α = 0.05, test to determine whether the introductory program provides a statistically significant weight loss. What is your conclusion?


Question 4
Safegate Foods, Inc., is redesigning the checkout lanes in its supermarkets throughout the country. Two designs have been suggested. Tests on customer checkout times have been conducted at two stores where the two new systems have been installed. A summary of the sample data follows.

System A System B
n1 = 120 n2 = 100
= 4.1 minutes
= 3.3 minutes

s1 = 2.2 minutes s2 = 1.5 minutes

Test at the .05 level of significance to determine whether there is a difference between the mean checkout times of the two systems. Which system is preferred?

Question 5
Samples of final examination scores for two statistics classes with different instructors provided the following results.

Instructor A Instructor B
n1 = 12 n2 = 15
= 72
= 78

s1 = 8 s2 = 10

With α = .05, test whether these data are sufficient to conclude that the mean grades for the two classes differ. Assume populations are normal with equal variances.

二、時機

社民連認為「五區總辭，全民公決」的時機，應該在政府提出 2012政改方案之前，甚至現在就可立即總辭。

香港特區政府 對於政改方案沒有絲毫主導權 已是眾所週知，而中央對於保留功能組別及分組點票，以及要用提名委員會 確保只有自己屬意的候選人 參加行政長官的意圖 更是彰彰明甚，是以，我們幾可確定，曾蔭權即將提出的方案是沒有路線圖之餘，其方案的本質也會一如 05年「循序漸退」。

因此，民主派 不必再隨特區政府的假諮詢起舞，盡快實行五區總辭，務必在政府將政改方案 提交立法會通過前使公投有結果。