Spots Statistics

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Q1: You are attending a championship soccer match with your family. In your pocket only $40 to spend on Popcorns(S) and Cokes (C), supposed to allocate such amount to maximize satisfaction of the two goods, where the price of popcorn is $5 and the price of coke is $4, looking at the table below:
Various levels of S and C MUs MUs/Ps MUc MUc/Pc
1 40 120
2 30 80
3 25 40
4 20 32
5 15 16
6 10 8
MUs = marginal utility of popcorn, Ps = price of popcorn
MUc = marginal utility of coke, Pc = piece of coke

Answer the followings:

  1. Fill up the blanks above?
  2. Find the combination of popcorns and cokes yields and the level of utility, subject to the budget constraint?
  3. Calculate the total utility of the optimal consumption of the two good?
  4. What is the marginal rate of substitution(MRS) in such case?
  5. State the budget equation in this case?
  6. Graph the budget line and an indifferent curve, showing the optimal point?
  7. What does the indifferent curve represent? How it relates to the indifference map?
  8. What is the level of marginal utility per dollar spent, where you get the maximization or the optimal equation of the two goods?
  9. The demand curve is derived from the marginal utility concept, explain?
  10. Can you classify this case as a corner solution? Explain?

Q2: Decided on open tailor shop, the following table gives the level of outputs(shirts) produced daily, with the least cost of input combinations (labor wage(w) = $300, and cost of capital, sewing machine(r) = $200) per day:
output Labor # Capital # Long run total cost (LTC) Long run average cost(LAC) Long run marginal cost(LMC)
100 10 7
200 12 8
300 20 10
400 30 15
500 40 22
600 50 30
700 60 42
Answer the followings:

  1. Fill up the blanks above?
  2. Write down the cost equation?
  3. State the total production function?
  4. Draw up the graph for LAC and LMC in relation to the output?
  5. Graph the Isoquant curve as well as the Isocost curve, with the optimal input combination?
  6. In this case, you are operating in competitive market, what are the characteristics of such market?
  7. At which price you are supposed to sell the shirt?
  8. Draw up the expansion path for outputs and costs in the table above?
  9. What is the approximate level of output(varies discretely by 100 units in the table), where profit is maximized and you are economically and technically efficient?
  10. What is the Marginal Rate of Technical Substitution (MRTS) in this case?
  11. Is the cost structure in the question long-run cost or short-run cost ones, what is the difference between the two, and how can they be related?
  12. There are many factors reduce costs, and shift LAC downtrend, identify three of them?
  13. At which level of output is the Minimum Efficient Scale(MES)?
  14. What kind of demand curve you are facing in this market?
  15. Is this competitive market, what is the economic profit, and should it be different in value from the opportunity cost? Explain?

Q3: Abdullah want to expand the capacity of his restaurant, but not sure of the 2020 economic growth (GDP) of the Saudi economy. He has the probability of 40% that the economy will maintain the expected growth rate in 2019 (1.8%) and the probability of 60% it will be little higher (2.1%) as the IMF forecasted. Accordingly, the table below is:
Growth rate 2.1% 1.8%
Probability Dist. 60% 40%
Profit Profit($Million) Profit($Million)
A. Decision maintain capacity 100 persons 3 2
B. Decision expand capacity by 20% 4 1
Answer the following:

  1. Compute the expected profits for both decisions?
  2. Based on the expected profit only, which decision should Abdullah make?
  3. Compute the Standard Deviation for decisions A and B, facing Abdullah?
  4. Which decision would Abdullah make, using the coefficient of variation?
  5. If Abdullah has no idea of the probability distribution of economic growth, operating in uncertainty world. Using the information above, what decision would Abdullah make, according to each of the following rules:
    A. Maximax:
    B. Maximin:
    C. Minimax Regret:
    D. Equal Probability:
  6. Which decision is riskier, and how can you classify yourself as risk lover or averter or neutral?

Sample Solution

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COVID huge backlog of demand for health and wellbeing services.

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Covid has created a huge backlog of demand for health and wellbeing services. You have been retained as an Innovation Management consultant by a local GP with the support of the local health board. Your brief is to develop an innovation to help reduce their waiting list, allowing them to prioritise the most urgent cases. Unfortunately, due to financial pressures, they are not in a position to provide additional resource. It is hoped that a successful intervention would have potential to be scaled rapidly across other GPs in order to maximise its benefit.

Sample Solution

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“for women who are never good enough” BY TRACY M Hallstead

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1.Pygmalion’s Chisel: “for women who are never good enough” BY TRACY M hallstead

Citation:
Hallstead, Tracy M.. Pygmalion’s Chisel : For Women Who Are “Never Good Enough”, Cambridge Scholars Publisher, 2013. ProQuest Ebook Central, https://ebookcentral.proquest.com/lib/tourony-ebooks/detail.action?docID=1220963.

  1. Galatea’s Emancipation: The Transformation of the Pygmalion Myth in Anglo-Saxon Literature since the 20th Century by: Stefanie Eck
    citation:
    Eck, Stefanie. Galatea’s Emancipation: The Transformation of the Pygmalion Myth in Anglo-Saxon Literature since the 20th Century, Diplomica Verlag, 2013. ProQuest Ebook Central, https://ebookcentral.proquest.com/lib/tourony-ebooks/detail.action?docID=1640382.
    PDF:
    Eck, Stefanie. Galatea’s Emancipation: The Transformation of the Pygmalion Myth in Anglo-Saxon Literature since the 20th Century, Diplomica Verlag, 2013. ProQuest Ebook Central, https://ebookcentral.proquest.com/lib/tourony-ebooks/detail.action?docID=1640382.

Sample Solution

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Problems; Partial

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For the next four problems just do the following:
(Answer any three of the four questions. If you answer a fourth question and identify that as an extra-credit question, it will be graded for four extra credit points)

A. Identify the independent variable(s) – if any (and define them precisely and indicate they are qualitative or quantitative)
B. Identify the dependent variable – if any (and define them precisely and indicate they are qualitative or quantitative)
C. Identify the type of analysis that is appropriate (Chi-Square test of independence, ANOVA, Regression, or Correlation)
D. Justify why the analysis you identified in part C is correct.
(3 + 3 + 3 + 3 points)

  1. Your firm is having quality problem with the production of plastic automotive parts: there are too many defectives. One of your engineers thinks that it’s because the temperature of the process is not controlled carefully enough. Another engineer is sure that it’s because the assembly line is being shut down too often for unrelated reasons. You have decided to analyze the problem and have come up with figures for the percent defective each day recently, the standard deviation of temperature measured hourly each day (as a measure of temperature control), and the number of assembly line stoppages each day. You are interested in finding out which engineer is right.

A.

B.

C.

D.

  1. Some critics of big business argue that CEOs are overpaid and that their compensation is not related the performance of their company. To test this theory, data on executive’s total pay and company’s performance was collected from a randomly selected set of fifty companies.

A.

B.

C.

D.
 

  1. Many companies use well-known celebrities in their ads, while other companies create their own spokespersons (such as Maytag repairman). A marketing researcher is interested in investigating the relationship between gender of the spokesperson and brand awareness. Three hundred television viewers were asked to identify the products advertised by celebrity spokespersons.

A.

B.

C.

D.

  1. To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, Jacob’s Chemical Company obtained the data on the mixing times from ten batches for each of the machines. What can we conclude?

A.

B.

C.

D.

Problems — Full

For the next two problems just do the following:

A. Set up the appropriate hypotheses (in plain English)
B. Draw appropriate statistical conclusions (based on the printout provided). In your conclusions, make sure to indicate what values you specifically used from the printout (i.e., highlight/mark/circle the relevant values you need from the printout and then use them in your discussion/conclusions).
C. Present proper conclusions for the business problem.

  1. As a consulting industrial engineer you are hired to perform a “human factors experiment” at Burstinter & Lobel, a large law firm. A pool of 30 typists of similar ability and experience is selected to participate. Groups of 10 typists each are randomly assigned to one of three working conditions—very noisy atmosphere (90 Db constant), somewhat noisy atmosphere (65 Db constant), and pleasant atmosphere (40 Db constant). The subjects are then asked to type a technical manuscript. The following data represent the number of mistakes on the manuscript make by the typists under the various working conditions. Groups
    Very Noisy
    (90 Db) Somewhat Noisy
    (65 Db) Pleasant
    (40 Db)
    14
    12
    13
    13
    16
    18
    19
    11
    10
    13 2
    5
    8
    5
    7
    6
    9
    4
    10
    9 2
    6
    6
    2
    4
    3
    2
    1
    7
    5 At the .01 level of significance, is there evidence of a difference in the average number of errors between the three groups?
    (3 + 8 + 6 points)

Please refer to Printout #1 for this problem

A. H0:

H1:

B.

C.

  1. A list of best selling cars for 1987 is shown in the table. The 1988 suggested retail price and the total number sold are given in the table below..

MODEL 1988 Price
(in thousands) Number sold
(in thousands)

Hyundai
Oldsmobile Cierra
Nissan Sentra
Ford Tempo
Chev. Corsica
Pontiac Grand Am
Toyota Camry
Chev. Caprice 5.4
11.4
6.4
9.1
10.0
10.3
11.2
12.5 264
245
236
219
214
211
187
177
At  = .05, is there evidence of relationship between the two variables?
(3 + 8 + 6 points)

Please refer to Printout #2 for this problem

A H0:

H1:

B.

C.

Essay Questions

  1. What is Post-ANOVA test? Why is it necessary? When? Explain with an example.
    (4 + 2 + 2 points)
  2. The heights of a sample of husbands and wives in the Heightlands are given below. Write down an equation (i.e., the regression equation) predicting the height of a husband (Y) from the height of his wife (X). What is the correlation coefficient for this equation? (2 + 2 points) Height of husband Height of wife
    72 67
    68 63
    63 58
    59 54

 
Printout #1
One-way ANOVA: Mistakes versus NoiseLevel
Method
Null hypothesis All means are equal
Alternative hypothesis Not all means are equal
Significance level α = 0.05
Equal variances were assumed for the analysis.
Factor Information
Factor Levels Values
NoiseLevel 3 1, 2, 3
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
NoiseLevel 2 546.9 273.433 42.19 0.000
Error 27 175.0 6.481
Total 29 721.9
Model Summary
S R-sq R-sq(adj) R-sq(pred)
2.54588 75.76% 73.96% 70.07%
Means
NoiseLevel N Mean StDev 95% CI
1 10 13.900 2.923 (12.248, 15.552)
2 10 6.500 2.550 (4.848, 8.152)
3 10 3.800 2.098 (2.148, 5.452)
Pooled StDev = 2.54588

Printout #2
Regression Analysis: Number versus Price
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 3311 3310.9 7.77 0.032
Price 1 3311 3310.9 7.77 0.032
Error 6 2556 426.0
Total 7 5867
Model Summary
S R-sq R-sq(adj) R-sq(pred)
20.6396 56.43% 49.17% 23.44%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 302.9 30.9 9.80 0.000
Price -8.78 3.15 -2.79 0.032 1.00
Regression Equation
Number = 302.9 – 8.78 Price
Fits and Diagnostics for Unusual Observations
Obs Number Fit Resid Std
Resid
2 245.0 202.8 42.2 2.30 R
R Large residual

Sample Solution

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