1. Lawson’s Department Store faces a buying decision for a seasonal product for which demand can be high or low. The purchaser for Lawson’s can order 1, 2, or 3 lots of the product before the season begins but cannot reorder later. Profit projections (in thousands of dollars) are shown.

1. Find the optimal decision using the expected value approach.
2. Use the expected loss opportunity method to find the Expected Value of Perfect Information.
3. Conduct a graphical sensitivity analysis identifying the decisions for the different P(S1).
4. For the optimal solution, given the current probabilities of the state of nature, what would be the range of optimality (that is the range of values for its payoff where that decision alternative will still remain optimal) for its payoffs compared to the closest Expected Value.

1) A researcher would like to determine if relaxation training affects the number of headaches for chronic headache sufferers. For a week prior to training, each participant records the number of headaches suffered. Participants then receive relaxation training and for the week following training the number of headaches is again measured. The data are as follows: before: 6, 5, 3, 3, 6, 2, 4, 4 and after: 4, 1, 3, 1, 2, 1, 3, 2.

a. Do the results indicate a significant difference? Use a two-tailed test with α = .05. State the null hypothesis and the tcritical you will use to evaluate the null hypothesis.

b. Compute Cohen’s d and r2 to measure the size of the effect. Conclude with a separate summary statement for each measure of effect size that is appropriate for publication in a scientific journal.

1. A management company must first decide whether to undertake a market research survey. If the market research study is conducted, the outcome will either be favorable (F) or unfavorable (U). Assume there are only two decision alternatives, D1 and D2, and two states of nature, S1 and S2. The payoff table showing profit is as follows:

1. Using the following probabilities, what is the optimal decision strategy?

P(F) = 0.56        P(S1/F) = 0.57               P(S1/U) = 0.18              P(S1) = 0.40

P(U) = 0.44       P(S2/F) = 0.43               P(S2/U) = 0.82             P(S2) = 0.60

2. Find the Efficiency of this market research. What would be your recommendation?
3. How much will this company be willing to pay for this market research?

1. Consider the following data set regarding six company employees who report to the same manager in a local office:

List the column letter(A,B,C,D,E,F) associated with the following questions.

a. Which variables arecategorical (qualitative)? Answer: ___________________

b. Which variables are numerical (quantitative)?Answer: ___________________

c. Which of the variables, if any, arediscrete?     Answer: ___________________

d. Which variables, if any, are continuous?         Answer: ___________________

e. Which variables, if any, requireanIntervalScale? Answer: ________________

f. Which variables, if any, requirean OrdinalScale? Answer: ________________

g. Which variables, if any, requirea NominalScale? Answer: ________________

h. Which variables, if any, requirea Ratio Scale?     Answer: _______________

Political parties want to know what groups of people support them. The General Social Survey (GSS) asked its 2014 sample, "Generally speaking, do you usually think of yourself as a Republican, Democrat, Independent, or what?" The GSS is essentially an SRS of American adults. Here is a large two-way tale breaking down the responses by the highest degree the subject held:

1. Make a 2x5 table by combining the counts in the three rows that mention Democrats, Republicans and ignoring strict independents and supporters of other parties. We might think of this table as comparing all adults who lean Democrat or Republican. How does does support for the two major parties differ among adults with different levels of education?

2. Use the full table to analyze the differences in political party support among levels of education. The sample is so large that the differences are bound to be highly significant. but give the χ2χ2 test statistic and p-value nonetheless. The main challenge is in seeing what the data say. Does the full table yield any insights not found in the compressed table analyzed in part 1?

The following are advertised sale prices of color televisions at an electronics store.

Calculate the least squares line. Put the equation in the form of:

ŷ = a + bx

Find the correlation coefficient r.

Find the estimated sale price for a 33-inch television. (Use your equation from part (d). Round your answer to two decimal places.)
$

Find the estimated sale price for a 47-inch television

What is the slope of the least squares (best-fit) line? (Round your answer to three decimal places.)

2. Suppose a randomly chosen group of 150 high school juniors and seniors who took the SAT twice over a period of six months showed an average improvement on the second SAT of 25 points. The standard deviation of the difference in the scores between the first and second SAT was 20 points.

a. What is the appropriate design for this situation?

b. Set up an appropriate hypotheses to test the claim that the score on the second SAT is, on average at least 20 points higher than on the first SAT.

c. Test the hypotheses stated in part b. What distribution should be used? What assumptions, if any, should be checked? Explain. Make a decision and give a conclusion.

The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $1600 and the standard deviation is $140.
1180 1320 1460 1600 1740 1880 2020


Use the 68-95-99.7 Rule to answer the following questions.

What is the approximate percentage of buyers who paid more than $2020?
%

What is the approximate percentage of buyers who paid more than $1880?
%

What is the approximate percentage of buyers who paid between $1460 and $1740?
%

What is the approximate percentage of buyers who paid between $1460 and $1600?
%

What is the approximate percentage of buyers who paid between $1600 and $2020?
%

What is the approximate percentage of buyers who paid between $1600 and $1880?

Price of eggs and milk: The following table presents the average price in dollars for a dozen eggs and a gallon of milk for each month from January through October

2010

.

If the price of eggs differs by $0.25 from one month to the next, by how much would you expect the price of milk to differ? Round the answer to two decimal places.

(3) (Continued from Question 2) Based on the sample of 10 men with ages and cholesterol levels given in the table in Question 2, answer the following.

(a) At 5% significance level, do the data provide sufficient evidence to conclude that age is useful as a (linear) predictor of cholesterol level? State any assumption(s) you make.

(b) What is the mean estimated cholesterol level for all 74 year old men?

(c) Find a 90% confidence interval for mean cholesterol level for all 74 year old men.

(d) Find a 90% prediction interval for mean cholesterol level for all 74 year old men.

(e) If we wish to add one dummy predictor variable to make a multiple regression model, what would it be?

please show me the math for this

The data

You have been given data from red maple and white oak trees from a national forest dominated by mixed hardwood stands.  The following variables for each tree are included

treecode,location,species,dbh,height
1-W-7,eastern,MR,46.8,39.2
1-N-1,eastern,MR,47.1,37.4
1-E-4,eastern,MR,60.6,41.1
2-M-2,eastern,MR,50.1,26.9
3-E-4,eastern,MR,16.4,25.2
3-M-6,eastern,MR,29.4,27.3
3-S-4,eastern,MR,33.3,38
3-N-5,eastern,MR,37.4,22.5
3-N-6,eastern,MR,36.4,25
4-M-3,eastern,MR,7.2,3.9
4-M-2,eastern,MR,8,6.1
5-E-3,eastern,MR,19.6,14.5
7-N-5,eastern,MR,41.6,34.1
8-W-5,eastern,MR,31.7,31
8-S-7,eastern,MR,39.4,31.2
11-M-3,eastern,MR,16.3,24.3
11-M-5,eastern,MR,22.8,26.2
11-M-8,eastern,MR,23.4,30.8
11-M-4,eastern,MR,29.5,25.6
11-N-7,eastern,MR,37.5,27.6
11-S-6,eastern,MR,40.4,34.8
13-M-3,eastern,MR,31.8,27.7
13-M-2,eastern,MR,67.4,37.8
14-M-5,eastern,MR,31.1,28.7
14-M-4,eastern,MR,35.4,30.6
14-W-2,eastern,MR,34.3,33.3
14-E-3,eastern,MR,41.5,32.4
14-N-3,eastern,MR,39.1,36.8
14-M-3,eastern,MR,51,43.4
42-N-1,western,MR,57.6,35.9
43-M-4,western,MR,2.5,4.8
43-M-5,western,MR,3.4,4.8
43-M-7,western,MR,7,7
43-M-9,western,MR,10.5,9.7
44-M-3,western,MR,18.2,22.3
44-E-3,western,MR,25.6,25.3
45-M-1,western,MR,62.7,40
46-M-1,western,MR,25.6,28.3
46-M-2,western,MR,28.7,26.6
46-M-5,western,MR,43.9,26.8
46-N-9,western,MR,50.9,36.1
46-M-7,western,MR,56.3,35.2
47-N-1,western,MR,8.6,8.7
47-E-4,western,MR,22.6,19.3
48-M-2,western,MR,26,21.6
48-S-5,western,MR,30.7,23.5
49-M-7,western,MR,38.3,26.8
49-W-1,western,MR,45.4,29.6
50-M-5,western,MR,27,19
3-W-5,eastern,OW,6,6.5
3-W-3,eastern,OW,12.5,7.8
3-M-4,eastern,OW,19.1,25.2
3-M-3,eastern,OW,34.4,25.2
7-M-3,eastern,OW,31.7,24.2
7-S-1,eastern,OW,40.2,23
7-N-6,eastern,OW,45.5,25.2
7-N-7,eastern,OW,52.4,31.3
7-W-5,eastern,OW,54.3,28.3
8-M-2,eastern,OW,37.8,30.9
8-E-1,eastern,OW,65,36.4
8-M-4,eastern,OW,68.1,32.2
9-S-6,eastern,OW,59.8,46.9
11-M-2,eastern,OW,12.1,18.6
11-E-2,eastern,OW,17.7,12.4
48-M-7,western,OW,62.5,27.6
49-M-8,western,OW,3.7,4.4
49-N-4,western,OW,47.8,19.5
49-M-6,western,OW,53.4,29.6
49-M-4,western,OW,56,25.3
49-M-3,western,OW,67.4,27.4
50-N-2,western,OW,45.4,20.8
50-M-7,western,OW,48.1,23.9
50-M-4,western,OW,45.4,23.4
50-M-2,western,OW,48.7,22.7
52-N-6,western,OW,5.2,7
53-E-2,western,OW,44.3,30.6
53-N-2,western,OW,45.3,23.7
53-M-5,western,OW,76.9,28.6
54-M-6,western,OW,32.7,23.3
54-M-2,western,OW,40.2,24.1
54-S-6,western,OW,47.8,26.1
55-M-1,western,OW,49,27
55-M-2,western,OW,66.3,26.7
56-M-3,western,OW,29.3,18.8
57-M-3,western,OW,37.9,37.4
58-M-6,western,OW,41.9,22.4
59-M-2,western,OW,24.7,15.1
61-M-6,western,OW,57.3,30.6
62-M-10,western,OW,4.1,8.3
62-M-2,western,OW,9.1,2.7

1. Read in the csv file into a dataframe called “trees” with either the Import utility in RStudio, or by using the function read.csv, e.g.:

trees = read.csv("C:/My Documents/ E-W MR-OW data.csv")

1. Examine the variables using the str function:

What kind of data is contained in the “species” variable?  What kind of data is contained in the height variable

2. Examine the first few lines of data using the head function:

head(trees)

The physicians in previous problem have been approached by a market research firm that offers to perform a study of the market at a fee of $5,000. The market researchers claim their experience enables them to use Bayes’ theorem to make the following statements of probability:

probability of a favorable market given a favorable study -----0.82 probability of an unfavorable market given a favorable study 0.18 probability of a favorable market given an unfavorable study 0.11 probability of an unfavorable market given an unfavorable

study-- 0.89 probability of a favorable research study ----------0.55 probability of an unfavorable research study----------------------0.45

a) Develop a new decision tree for the medical professionals to reflect the options now open with the market study.

b) Use the EMV approach to recommend a strategy.
c) What is the expected value of sample information? How much might the

physicians be willing to pay for a market study?
d) Calculate the efficiency of this sample information.

5. Speed (mph) Braking Distance (ft) 30 40 50 60 70 80
48 79 123 184 243 315. Find the Sx, Sy, Find correlation coefficient, regression line y.

The Titanic Used the data in the following table, which summarizes results from the sinking of the titanic.

1. If one of the Titanic passengers is randomly selected, find the probability of getting someone who is a women or survivor.
2. If one of the Titanic passengers is randomly selected, find the probability of getting a man and someone who survived the sinking.
3. If one of the Titanic passengers is randomly selected, find the probability of getting a boy or girl?
4. If one of the Titanic passengers is randomly selected, find the probability of getting a man, given that the selected person died.
5. If Three of the Titanic passengers is randomly selected, find the probability of all three are boys?