Problem 4-11 (Algorithmic)

Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows:

Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows:

If the Edwards production plan for the next period includes 1025 units of component 1 and 825 units of component 2, what purchases do you recommend? That is, how many units of each component should be ordered from each supplier? Round your answers to the nearest whole number. If your answer is zero, enter "0".

What is the total purchase cost for the components? Round your answer to the nearest dollar.

$ ____________

Please answer the following questions based on the analysis in excel.

1. Calculate the mean, standard deviation, and variance of the two samples. Embed the answers in the data sheet.

2. Calculate the degrees of freedom for a t test assuming the population standard deviation is unknown with unequal variance between samples.

3. Perform a two-tailed two-sample mean test assuming the population standard deviation is unknown with unequal variance. (.01 significance level)

4. State your conclusion from the two-tailed test.

In Texas Hold’em, each player is dealt two cards from the deck. Obviously, this is done without replacement, so you cannot use the binomial distribution. You can use the hypergeometric distribution or reason from first principles.

a) What is the probability of being dealt a pair? Express it as an exact fraction and an approximate percentage.

b) If you are dealt two unpaired cards, say the ace of clubs and the 8 of diamonds, what is the chance of getting a pair or better on the flop? The flop is three cards dealt all at once, and we want to know the chance that the flop will contain at least one ace or at least one 8.

3. You also have been asked to determine at both the 2% and 5% levels of significance whether the proportion of supporters of the candidate that describes itself as generally loyal to the political party of the candidate has decreased recently from its previously hypothesized value of 80%. You select a random sample of supporters of the candidate for study. The sample data concerning whether the supporters generally describe themselves as party loyalists is shown below. Answer the question as to whether there has been a decrease in the population proportion of supporters that describes itself as party loyalists from its previous value of 80%.

Appendix Two: Party Loyalist? (Y = yes, N = no)

Y         Y         Y         N         Y         N         Y         N         Y         N         Y

N         Y         Y         Y         Y         Y         N         N         N         Y         Y

Y         Y         Y         Y         Y         Y         Y         Y         Y         Y         Y

N         Y         N         N         Y         N         Y         Y         N         Y         N

Y         N         N         N         Y         Y         Y         N         Y         Y         N

One genetic disease was tested positive in both parents of one family. It has been known that any child in this family has a 25% risk of inheriting this disease. A family has three children. The probability of this family having one child who inherited this genetic disease is:

The risk of HIV:

The risk of HIV runs high in North America. In the at-risk population, about 1 in 30 people are HIV carriers, while in general population (people who are not at risk), 1 in 300 are. The at-risk population is 2% in total in North America. Doctors have developed a test for HIV and suppose that it correctly identifies carriers 95% of the time, while it correctly identifies the disease-free only 90%. As the test detects HIV only, you can assume that it is conditionally independent of being at risk, given carrier or not-carrier status.

a. If a random person is sampled, what is the probability that he/she is a carrier?

b. Given that a person has a positive test result and is not in the at-risk population, what is the probability that he/she is a carrier?

How would bias impact developing of accurate predictive models? How would you minimize the impact of bias?

Hypotheses can be written as questions, statements and equality/inequalities. To be truly proficient, you must be able to interpret a hypothesis, regardless of how it is expressed.

A financial planning firm has a decision to make. The company can buy more stocks (B) now, not buy and not sell stock (N) now, or it can sell its stock (S) now.

The following is from the Google Dictionary:

Bear Market: a market in which prices are falling, encouraging selling.

Bull Market: a market in which share prices are rising, encouraging buying.

The future market will be either Bear (E) or Bull (U).

The following is a payoff table, in thousands of dollars, of profit or loss for this firm based on the decision the firm makes now and the future market.

The statisticians of the company, using their standard budget, predict the following probabilities:

P(E) = 0.72                                      P(U) = Complement

The statisticians report that if the company is charged and additional $5,000 above the standard fee, they can do more accurate research to obtain sample information that will either be Favorable (F) or Unfavorable (X) with the following probabilities:

P(F) = 0.7                                        P(X) = Complement

If the research is favorable, the revised probabilities are:

P(E) = 0.82                                     P(U) = Complement

If the research is unfavorable, the revised probabilities are:

P(E) = 0.31                                P(U) = Complement

Do all calculations, including making the decision tree and any algebra, in Excel; organize it and highlight important boxes in colors so that it can be read and understood very easily. Put question numbers next to the answers. You may want to use multiple sheets, but please use only one file. Write out all answers, including #15 and #21 in Excel. For all algebra, show work [the written steps you went through to find the answer] and type that into Excel. Do not submit the paper you may have used to solve the algebra, just copy it and put it all in Excel.

Very Important: Input the data only once. After that, link all calculations from new cells to previous cells, as illustrated in of the videos. Answers to questions that have the right number but are not linked will be marked incorrect. Projects that do not link cells will receive a very low grade.

Please complete the following in Excel, highlighting the answers.

Find the following:          [The number in the brackets is how many points each question is worth.]

1. The decision using the optimistic approach. [2]
2. The decision using the conservative approach. [2]
3. The decision using the minimax regret approach. [2]
4. The decision using the Expected Opportunity Loss (EOL) [2]
5. EV(B) [1]
6. EV(N) [1]
7. EV(S) [1]
8. Best EMV = The decision using EV [1]
9. EVwPI [1]
10. EVPI [1]

For #11 and #12: make three comparisons, EV(B) to EV(N), EV(B) to EV(S), EV(N) to EV(S). You will have three cutoff points and four test points.

11. The value of probability (p) of E that is the cut off for changing the best decision. [4]
12. Draw a number line for #11. [4] (sensitivity analysis)
13. The value for which the payoff of E of the best decision must be greater than to keep the best decision the same. [4] (sensitivity analysis)
14. The value for which the payoff of U of the best decision must be greater than to keep the best decision the same. [4] (sensitivity analysis)
15. Rank p, payoff of E, and payoff of U from least to most sensitive and explain why. Make sure to rank them and explain why you have chosen your order. [2]
16. The decision tree [6]
17. EVwSI [1]
18. EVSI [1]
19. Efficiency of the Sample Information [2]
20. The Risk Profile [4]
21. Based on the cost of obtaining the sample information and its efficiency, is it worth obtaining it? Why? Please include ALL the relevant information for this decision and use specific numbers. Your answer must discuss EVSI, net EVSI (The EVSI minus the cost of the SI), the Efficiency of the Sample Information (abbreviated "E") and the Risk Profile. This is the most important question in the project, as you are making the decision to purchase the SI using all you have learned. Answers that do not include all this will not get credit. [4]

A professor has learned that eight students in her class of 31 will cheat on the exam. She decides to focus her attention on ten randomly chosen students during the exam.

a. What is the probability that she finds at least one of the students cheating? (Round your final answers to 4 decimal places.)

b. What is the probability that she finds at least one of the students cheating if she focuses on eleven randomly chosen students? (Round your final answers to 4 decimal places.)

1. A process is in statistical control with   and The control chart uses a sample size of n = 3. Specifications are at 42 ± 4. The quality characteristic is normally distributed.

1. What conditions should we check to ensure that conclusions from a capability analysis are correct?

2. Estimate the potential capability of the process.

3. Estimate the actual capability of the process.

4. How much improvement in ppm could be made in process performance if the mean could be centered at the nominal value?

An investor owns a portfolio consisting of two mutual funds, A and B, with 50% invested in A. The following table lists the inputs for these funds.

a. Calculate the expected value for the portfolio return. (Round your answer to 2 decimal places.)

Expected Value:

b. Calculate the standard deviation for the portfolio return. (Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.)

Standard Deviation:

14.Waiting times​ (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the coefficient of variation for each of the two sets of​ data, then compare the variation

The coefficient of variation for the waiting times at Bank A is ____%.

​(Round to one decimal place as​ needed.)

The coefficient of variation for the waiting times at the Bank B is ____.

​(Round to one decimal place as​ needed.)

Is there a difference in variation between the two data​ sets?

A.There is no significant difference in the variations.

B.The waiting times at Bank B have considerably less variation than the waiting times at Bank A.

c.The waiting times at Bank A have considerably less variation than the waiting times at Bank B.

In the book Business Research Methods, Donald R. Cooper and C. William Emory (1995) discuss a manager who wishes to compare the effectiveness of two methods for training new salespeople. The authors describe the situation as follows:

The company selects 22 sales trainees who are randomly divided into two equal experimental groups—one receives type A and the other type B training. The salespeople are then assigned and managed without regard to the training they have received. At the year’s end, the manager reviews the performances of salespeople in these groups and finds the following results:

(a) Set up the null and alternative hypotheses needed to attempt to establish that type A training results in higher mean weekly sales than does type B training.

H₀: µ_A ? µ_B ?  versus H_a: µ_A ? µ_B  >

(b) Because different sales trainees are assigned to the two experimental groups, it is reasonable to believe that the two samples are independent. Assuming that the normality assumption holds, and using the equal variances procedure, test the hypotheses you set up in part a at level of significance .10, .05, .01 and .001. How much evidence is there that type A training produces results that are superior to those of type B? (Round your answer to 3 decimal places.)

(c) Use the equal variances procedure to calculate a 95 percent confidence interval for the difference between the mean weekly sales obtained when type A training is used and the mean weekly sales obtained when type B training is used. Interpret this interval. (Round your answer to 2 decimal places.)

Confidence interval [, ]