# Parameters

Acme plumbing supply just received a shipment of 5,000 stainless steel valves, but 50 regular steel valves were also sent. There is no way to tell the difference between the valves. A customer orders 5 stainless steel valves . What is the probability that one or more will be regular steel? What distribution will be used? What are the parameters? Represent the question as a probability statement? Calculate the probability?

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#### Solution Preview

This is a binomial distribution, which gives the discrete probability distribution of obtaining exactly n successes out of N trials.

<br>The formula is given by: P(n|N)=[N!/n!(N-n)!] p^n (1-p)^(N-n)

<br>Where n is the number of regular valves that ...

#### Solution Summary

The soltuion addresses Acme plumbing supply just received a shipment of 5,000 stainless steel valves, but 50 regular steel valves were also sent. There is no way to tell the difference between the valves. A customer orders 5 stainless steel valves . What is the probability that one or more will be regular steel? What distribution will be used? What are the parameters? Represent the question as a probability statement? Calculate the probability?

Forecasting & Regression (12 Problems) : Hypothesis Testing and 2- and 3-Parameter Exponential Smoothing

On multiple choice, check any appropriate answers. For any hypothesis tests, use a .05 level of significance.

Barrel temp.

(in oF) Mold temp.

(in oF) Injection pres. (in psi) Strength

(psi)

320 100 7000 3877

320 100 5000 3901

320 100 3000 4010

320 125 7000 3706

320 125 5000 3708

320 125 3000 4140

320 150 7000 3749

320 150 5000 3883

320 150 3000 4440

370 100 7000 4017

370 100 5000 4090

370 100 3000 3900

370 125 7000 3947

370 125 5000 4034

370 125 3000 4419

370 150 7000 4003

370 150 5000 3910

370 150 3000 4095

420 100 7000 3885

420 100 5000 4076

420 100 3000 4254

420 125 7000 4123

420 125 5000 4446

420 125 3000 4289

420 150 7000 4151

420 150 5000 4287

420 150 3000 4498

The data above represent test results for glass-reinforced plastic material. The production manager is trying to determine the appropriate settings for this process. In this experiment, he used three levels of barrel temperature (320, 370, and 420), three levels of mold temperature (100, 125, and 150), and three levels of injection pressure (7000, 5000, and 3000). The response is the material strength, and higher strengths are desired. Your job is to perform a multiple regression analysis to determine what settings should be used. You will use your output to answer the following questions.

1. We would conclude that the overall model (using all three explanatory variables) is statistically significant.

a. true

b. false

2. None of the explanatory variables are useful predictors.

a. true

b. false

3. The most useful predictor in the presence of the other explanatory variables is __________.

4. Multicollinearity is

a. severe.

b. mild.

c. nonexistent.

5. Which of the following combinations would be expected to yield the worst strength? Values are barrel temp., mold temp., injection pres.

a. 320, 100, 7000

b. 320, 125, 3000

c. 420, 150, 3000

d. 420, 100, 5000

e. 420, 100, 7000

6. Suppose you could use the following settings: (550, 250, 2000). These settings would

a. be preferable to any combination in #5.

b. yield results worse than any combination in #5.

c. be difficult to assess given the data we have.

7. You are comparing three multiple regression models for the same set of data, and you have the following available.

Model 1 Model 2 Model 3

X-variables 6 4 3

R2 .9344 .9277 .8761

Adjusted R2 .9058 .9133 .8497

MSE 5867.53 5746.09 5844.78

a. Model 1 performs the best in all areas.

b. Model 3 performs better than Model 2.

c. We would most likely prefer Model 1.

d. We would most likely prefer Model 2.

e. We would most likely prefer Model 3.

You are the newly hired manager of Simpson's, Inc., a small company that produces nonwoven fabric. You are currently trying to determine the number of rolls of fabric to produce during the first quarter of the next year for Burns & Smithers. You have collected data from the past 24 quarters, and are currently analyzing it. The data are given in the following table. How many rolls should you produce?

Quarter # of rolls ordered

1 56

2 48

3 58

4 67

5 59

6 51

7 64

8 71

9 73

10 67

11 78

12 84

13 77

14 70

15 82

16 89

17 83

18 74

19 84

20 93

21 86

22 78

23 85

24 93

8. Use single-parameter exponential smoothing with α = .2. This model

a. is effective

b. is appropriate

c. tends to underpredict

d. tends to overpredict

9. In the previous problem, suppose we used a different value of α. This change would

a. generate an appropriate model

b. possibly generate a better model (with respect to prediction)

c. tend to underpredict

d. tend to overpredict

10. Use a 2-parameter exponential smoothing model with α = .2 and

γ = .4. Next, use a 3-parameter exponential smoothing model with α = .2, γ = .4, and β = .7. Which of the following are true?

a. The 2-parameter model is most appropriate.

b. Both the 2 and 3-parameter models are more appropriate than the single-parameter model.

c. The 3-parameter model has the best fit to the data.

d. None of the exponential smoothing models are appropriate.

e. A classical decomposition model would be appropriate for this data.

f. An appropriate model will always give the best fit.

11. You are tracking mall sales over a two-year period.

a. The data will surely contain a trend component.

b. The data will likely contain a verifiable seasonal component.

12. In #11, suppose we track sales over a one-year period.

a. The data will surely contain an irregular (random) component.

b. The data will likely contain a verifiable seasonal component.