Verification and Validation of Simulation Models

3. How to build a model that is well connected with the verification and validation process?

4. What is meant by calibration, and what is the process of calibration so that it can obtain a model that means to be used for simulation?

In the United States, males between the ages of 40 and 49 eat on average 105.1 g of fat every day with a standard deviation of 4.5 g ("What we eat," 2012). Assume that the amount of fat a person eats is normally distributed. (a) State the random variable. (b) Find the probability that a man age 40-49 in the U.S. eats more than 110 g of fat every day. (c) Find the probability that a man age 40-49 in the U.S. eats less than 93 g of fat every day. (d) Find the probability that a man age 40-49 in the U.S. eats between 65 g and 100 g of fat every day. (e) If you found a man age 40-49 in the U.S. who says he eats less than 65 g of fat every day, would you believe him? Why or why not? (f) What daily fat level do 95% of all men age 40-49 in the U.S. eat less than?

In the United States, males between the ages of 40 and 49 eat on average 105.1 g of fat every day with a standard deviation of 4.5 g ("What we eat," 2012). Assume that the amount of fat a person eats is normally distributed. (a) State the random variable. (b) Find the probability that a man age 40-49 in the U.S. eats more than 110 g of fat every day. (c) Find the probability that a man age 40-49 in the U.S. eats less than 93 g of fat every day. (d) Find the probability that a man age 40-49 in the U.S. eats between 65 g and 100 g of fat every day. (e) If you found a man age 40-49 in the U.S. who says he eats less than 65 g of fat every day, would you believe him? Why or why not? (f) What daily fat level do 95% of all men age 40-49 in the U.S. eat less than?

Can someone please answer the following 10 Multiple choice questions? Thank you.

1. An analyst needs to build a forecasting model but he is not sure whether it has trend or seasonality components. Which of the following can help the analyst build decide on the forecasting model. Check all that apply.

2. _____ distribution is a _____  probability distribution whose mean equals its variance.

3 . After building a linear regression model, an analyst examined the residuals, which seemed to not be uniformly spread around the regression line, but rather seemed to spread around a curve. Which of the following, the should analyst consider?

4. An alternative medicine researcher is studying whether a newly developed herbal extract lowers blood pressure. Which one of the following confidence interval analyses can help the researcher in her study?

5. Poisson distribution can be used to model _____.

6. Assume you are working on a forecasting project, where you are expecting extreme outliers. Which one of the following forecast error measures should you consider? Why?

7. A group of researchers are studying the difference in the highway gas mileage of the new releases of 2 different car models from 2 different manufacturers, namely Toyota Corolla and Honda Civic. Which one of the following confidence interval analyses can help the researchers in their study?

8. An analyst is studying the relationship between the overall productivity of a manufacturing facility and the length of the workers' shift. The analyst decided to apply linear regression analysis to a data set from 91 different manufacturing facilities that belong to the same manufacturer and produce the same type of product. The facilities have different shift lengths, which are between 4 hours and 11 hours. The regression statistics and ANOVA returned acceptable values. Which of the following helps the analyst the most in deciding the relationship between productivity and shift length?

9. Assume you are working on an optimization problem where the fraction of sulfur in a new chemical product has to be constrained so it does not exceed 10%. There are 2 ingredient of the product and both of them contain sulfur. The amounts used from these 2 ingredients are denoted X and Y. These 2 ingredients contain 12% and 5% sulfur, respectively. Which of the following correctly expresses the constraint? Check all that apply.

10 An R&D engineer is in the process of building a forecasting model for a business problems. He consulted an expert from the operations department of his company. The expert expressed that the business logic dictates that the data series used in the forecasting model is highly expected to incorporate correlations between consecutive values for 2 lags. Which of the following models should the engineer choose?

Suppose a random variable, x, arises from a binomial experiment. If n = 22, and p = 0.85, find the following probabilities using any method of your choosing (e.g., the binomial formula; Excel, the TI 84 calculator). (a) P (x = 18) (b) P (x = 5) (c) P (x = 20) (d) P (x ≤ 3) (e) P (x ≥ 18) (f) P (x ≥ 20)

Airlines have increasingly outsourced the maintenance of their planes to other companies. A concern voiced by critics is that the maintenance may be less carefully done so that outsourcing creates a safety hazard. In addition, flight delays are often due to maintenance problems, so one might look at government data on percent of major maintenance outsourced and percent of flight delays blamed on the airline to determine if these concerns are justified. This was done, and data from 2005 and 2006 appeared to justify the concerns of the critics. Do more recent data still support the concerns of the critics? Here are data from 2014:

Make a scatterplot with outsourcing percent as ?x and delay percent as ?.

Find the correlation ?r with and without Hawaiian Airlines. Enter your answers rounded to four decimal places.

An ANOVA F test is an extension of a

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Question 2 (2 points)

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A manufacturer of infant formula is running an experiment using the standard (control) formulation and two new formulations, A and B. The goal is to boost the immune system in young children. There are 120 children in the study, and they are randomly assigned, 40 to each of the three feeding groups. The study is run for twelve weeks. The variable measured is Total IGA in mg per dl. It is measured at the end of the study, with higher values being more desirable. We are going to run a one-way ANOVA on these data. The hypotheses tested by the one-way ANOVA F test are

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Question 3 (2 points)

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At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the age (in weeks) at which their child was first able to creep or crawl a distance of four feet within one minute. The resulting data were grouped by month of birth. The data are for January, May, and September.

Crawling age is given in weeks. Assume that data are three independent SRSs, one from each of the three populations (babies born in a particular month), and that the populations of crawling ages have Normal distributions. The overall mean response is:

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Question 4 (2 points)

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I have three groups for which I want to perform an ANOVA. They have standard deviations s1 = 2.5, s2 = 3.4, s3 = 6.4 and the plots of the data indicate all samples are approximately Normal with no outliers. Is the ANOVA appropriate?

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Question 5 (2 points)

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A researcher is studying treatments for agoraphobia with panic disorder. The treatments are to be the drug Imipramine at the two doses 1.5 mg per kg of body weight and 2.5 mg per kg of body weight. There will also be a control group given a placebo. Thirty patients were randomly divided into three groups of ten each. One group was assigned to the control, and the other two groups were assigned to the two drug treatments. After twenty-four weeks on treatment, each of the subject's symptoms were evaluated through a battery of psychological tests, where high scores indicate a lessening of symptoms. Assume the data for the three groups are independent and approximately Normal with the same variance. An ANOVA F test tested the null hypothesis that there were no differences among the means for the three treatments that had a P-value less than 0.001. Which conclusion is correct?

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For the qualitative data, choose one of the outcomes and find the sample proportion satisfying that outcome. Now construct a 95% Confidence Interval of the Population Proportion of people satisfying that outcome.

Data Description: So there were 49 states counted for and of that 49 there were 3 states where the male population was greater than the females and there were 36 states where the female population was greater than the males and lastly there were 10 states where both populations were equal.

a. What is data mining?

b. What is specification searching?

c. Engaging in such behavior when conducting empirical research is generally viewed negatively? Why?

Automated manufacturing operations are quite precise but still vary, often with distributions that are close to Normal. The width in inches of slots cut by a milling machine follows approximately the N(0.8750,0.0014)

distribution. The specifications allow slot widths between 0.8725 and 0.8775 inch.

What proportion (±

0.001) of slots meet these specifications (use software)?

1. Run a simple regression using payroll in thousands to predict workers compensation premiums in thousands with a 99% confidence interval.

a. Please explain to the risk manager how useful this model is. (1 point)

b. Interpret the relationship between the independent variable and the dependent variable in terms of the coefficients. (1 point)

2. Run a multiple regression using both number of payroll in thousands and the indicator variable manufacturing to predict workers compensation premiums.

a. Please explain how useful this model is to the risk manager. (1 point)

b.Write out the estimated regression equation in terms of Y = a+b₁X₁+b₂X₂ (1 point)

c. Are both independent variables useful in predicting workers compensation premiums? Please explain why or why not? (2 points)

d. Interpret the relationship between each independent variable and the dependent variable in terms of the coefficients. (2 points)

e. Explain specifically how confident you are with regard to each of the coefficients of the model (using 95% confident interval). (2 points)

3. Run a multiple regression using all three independent variables: payroll, manufacturing, and metropolitan. Are all three variables useful in predicting workers compensation premiums? Please explain why or why not. (1.5 points)

4. Compare all three models - which one is the best? Please explain why. (1 point)

5. Using the best model, predict the manufacturing company’s workers compensation premiums assuming payroll of $850,000 and that the company is a manufacturing company. (1.5 points)

Data:

We want to compare the mean of the hospital stay by sex at this particular Pennsylvania hospital. Let’s assume that the data are normally distributed and we are assuming that the SD for sexes are equal.    So, is there a difference in the mean hospital stay in Pennsylvania hospital by gender?    (Please include SPSS output here)

State the null and alternative hypotheses.   

What is your test statistics and why?  (no calculation needed)

What were your test statistics results? What is your conclusion?

Please note: the table below might not be needed; however, these are my calculations for Mean and SD for sexes.

Part 1. Demonstrate that you understand basic concept of Normal Distribution. In two small paragraphs describe a couple of properties/rules of Normal distribution. Hint: look for KEY FACTS and DEFINITIONS in sections 6.1 and 6.2 of eText. Give one example of some practical case where we can use Normal distribution (for instance, IQ scores follow a normal distribution of probabilities with the mean IQ of 100 and a standard deviation around the mean of about 15 IQ points.) Part 2. Assign your numbers for mean μ and standard deviation σ. Make sure μ is about four times bigger than σ. Then select any number "a" below or above mean μ, but not too far from μ , difference (a - μ) should be less than 3σ. For example, μ = 80, σ = 20, a = 90 (or a = 75). Find following two probabilities: 1) P(x < a) 2) P(x > a) First, use formula: z = (a - μ)/σ to calculate z-value and then use Appendix Table for Standard Normal Distribution. You can find tables in Appendix to our eText or attached below. Remember, Appendix Table gives you probability P(xa) use formula: P(x>a) = 1 - P(x