# Testing hypotheses of more population means

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(1) The Ferguson Paper Company produces rolls of paper for use in adding machines, desk calculators, and cash registers. The rolls, which are 200 feet long, are produced in widths of 1 ½, 2 ½, and 3 ½ inches. The production process provides 200-foot rolls in 10-inch widths only. The firm must therefore cut the rolls to the desired final product sizes. The seven cutting alternatives and the amount of waste generated by each are as follows.

Cutting Alternatives Number of Rolls Waste (inches)

1 ½ in. 2 ½ in. 3 ½ in.

1 6 0 0 1

2 0 4 0 0

3 2 0 2 0

4 0 1 2 ½

5 1 3 0 1

6 1 2 1 0

7 4 0 1 ½

The minimum requirements for the three products are

Roll Width (inches) 1 ½ 2 ½ 3 ½

Units 1000 2000 4000

a. If the company wants to minimize the number of 10-inch rolls that must be manufactured, how many 10-inch rolls will be processed on each cutting alternative? How many rolls are required, and what is the total waste (inches)?

b. If the company wants to minimize the waste generated, how many 10-inch units will be processed on each cutting alternative? How many rolls are required, and what is the total waste (inches)?

c. What are the differences in approaches (a) and (b) to this problem? In this case, which objective do you prefer? Explain. What types of situations would make the other objective more desirable?

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The solution contains detailed explanation of testing whether the population means are the same.

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(1) The Ferguson Paper Company produces rolls of paper for use in adding machines, desk calculators, and cash registers. The rolls, which are 200 feet long, are produced in widths of 1 ½, 2 ½, and 3 ½ inches. The production process provides 200-foot rolls in 10-inch widths only. The firm must therefore cut the rolls to the desired final product sizes. The seven cutting alternatives and the amount of waste generated by each are as follows.

Cutting Alternatives Number of Rolls Waste (inches)

1 ½ in. 2 ½ in. 3 ½ in.

1 6 0 0 1

2 0 4 0 0

3 2 0 2 0

4 0 1 2 ½

5 1 3 0 1

6 1 2 1 0

7 4 0 1 ½

The minimum requirements for the three products are

Roll Width (inches) 1 ½ 2 ½ 3 ...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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