Multiple Sample

1. One Sample Test (15 pts.)

a) The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 99% confident in her decision, what conclusion can she make?

b) A major DVD rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. State the test of interest to the rental chain.

2. Two Sample Test (30 pts.)

a) To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Prove statistically whether the prep course is effective or not.

Exam Score Exam Score

Student Before Course (1) After Course (2)

1 530 670

3. 690 770

4. 910 1,000

5. 700 710

6. 450 550

7. 820 870

8. 820 770

9. 630 610

b) A few years ago, Pepsi invited consumers to take the "Pepsi Challenge." Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interested in determining what factors played a role in people's taste preferences. One of the factors studied was the gender of the consumer. Below are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi.

Males: n = 109, pM = 0.422018 Females: n = 52, pF = 0.25

c) The use of preservatives by food processors has become a controversial issue. Suppose 2 preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below.

Preservative I Preservative II

X

I = 106.4 hours

X

II = 96.54 hours

SI = 10.3 hours SII = 13.4 hours

3. Multiple Sample Test (20 pts.)

An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields, 5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a completely randomized design, the results are presented in the table that follows. Statistically analyze three samples.

Trial Smith Walsh Trevor

1 11.1 19.0 14.6

2 13.5 18.0 15.7

3 15.3 19.8 16.8

4 14.6 19.6 16.7

5 9.8 16.6 15.2

4. Relationship Test (10 pts.)

Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the 4 procedures, and collects the following numbers of patients from their own records. Is there a significant relationship between the return of the patient and surgical procedures at the significance level of 0.05?

	Procedure
	A	B	C	D	Total
Clear	27	41	21	7	96
Return	11	15	9	11	46
Total	38	56	30	18	142

5. Multiple Regression (15 pts.)

Type 0: one story house, type 1: two story house, Time: years since last assessment.

Construct a multiple regression equation and predict the vale of a two story house that was assessed to be $170,000 5 years ago.

Price($000)	Assessed Value	Type	Time
194.10	178.17	0	10
201.90	180.24	0	10
188.65	174.03	1	11
215.50	186.31	1	2
187.50	175.22	1	5
172.00	165.54	1	4
191.50	172.43	1	17
213.90	185.61	1	13
169.34	160.80	1	6
196.90	181.88	0	5
196.00	179.11	1	7
161.90	159.93	1	4
193.00	175.27	1	11
209.50	185.88	0	10
193.75	176.64	1	17
206.70	184.36	1	12
181.50	172.94	1	5
194.50	176.50	0	14
169.00	166.28	1	1
196.90	179.74	0	3
186.50	172.78	1	14
197.90	177.90	0	12
183.00	174.31	1	11
197.30	179.85	0	12
200.80	184.78	0	2
197.90	181.61	0	6
190.50	174.92	1	12
197.00	179.98	0	4
192.00	177.96	1	9
195.90	179.07	0	12

6. The maker of a packaged candy wants to evaluate the quality of her production process. On each of 16 consecutive days, she samples 600 bags of candy and determines the number in each day's sample that she considers to be of poor quality. The data that she developed follow.

Does she need to be concerned? (10 pts.)

Number Proportion

Day Poor Poor

1 33 0.0550000

2 29 0.0483333

3 31 0.0516667

4 32 0.0533333

5 43 0.0716667

6 45 0.0750000

7 46 0.0766667

8 48 0.0800000

9 48 0.0800000

10 46 0.0766667

11 28 0.0466667

12 32 0.0533333

13 28 0.0466667

14 32 0.0533333

15 31 0.0516667

16 24 0.0400000

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