QUESTION 1
Four factors are thought to possibly influence the taste of a soft-drink beverage: type of sweetener (A), ratio of syrup to water (B), carbonation level (C), and temperature (D). Each factor can be run at two levels, producing a 24 design. At each run in the design, samples of the beverage are given to a test panel consisting of 20 people. Each tester assigns a point score from 1 to 10 to the beverage. Total score is the response variable, and the objective is to find a formulation that maximizes total score. Two replicates of this design are run, and the results are shown below.
Attachments:
Write a report which critically evaluates and analyses a process and provides recommendations on how the process can be improved.
Complete the following tasks based on the unique data set you generated. These questions should be answered in a Word document, with brief reasoning to justify your answers. Your answers and reasoning should correlate with the tables and graphs from the excel sheet.
A. Draw a random sample of two hundred and fifty (250) households as per the Sample Selection Procedure. What sampling method have you used to select your sample data? In your opinion, is this the best method of sampling particularly when one is interested in characteristics like the gender of the household head, education levels etc., why or why not?
B. Compute the descriptive statistics and draw a Box-Whisker plot of Expenditures on the following variables (all series in one graph!);
(i) Alcohol (ii) Meals (iii) Fuel (iv) Phone
C.Use information from the descriptive statistics and the boxplots in part (B) above to present a summary of your findings by contrasting different features of these distributions.
A. Compute the top 10% value and the bottom 10% value of the household’s annual after-tax income (AtaxInc). What do these two values imply in terms of the distribution of the after-tax income?
B. The series OwnHouserepresents whether a household owns a house or not, that is a qualitative variable. Find the proportion of the households who own a house in your sample and use this proportion to find the probability that any three of the five randomly chosen households will own a house.
C. Draw a scatter plot of the natural log of total expenditures against the natural log of after-tax income, that is, ln(Texp) against ln(Ataxinc) and compute the coefficient of correlation. Express your finding of the linear relationship between the two variables.
A. Construct a contingency table between the gender and the level of education.
B. What is the probability that a random head of a household is a male and his higher level of education is Master?
C. What is the probability that the head of household is a male among those who have the Master degree?
D. What is the proportion of having the Bachelor as the highest degree from among females?
E. Do you think that the events “gender of household head is female” and “Primary” are independent?
Attachments:
1. Document a complete and thorough answer to Class Discussion Item 9.10.
2. Draw a schematic diagram illustrating the wiring of a Wheatstone bridge circuit that takes advantage of both three-wire lead connections and dummy gage temperature compensation.
3. A strain gage bridge used in a load cell dissipates energy. Why? Compare the power dissipated in a bridge circuit with equal resistance arms for gages of 350 Ω and 120 Ω when the excitation voltage is 10 V. What strategies can one employ if heating becomes a problem? Do these strategies have any deficiencies?
Evaluate the challenges of conducting quantitative research. Synthesize your findings and determine an appropriate quantitative research strategy for a study on employment discrimination. Analyze the issues associated with sampling, validity, reliability, and bias within the context of this study.
Need to know how to come up with answer given:
Suppose A and B live in an exchange economy with two goods x1 and x2. A owns 50 of both goods, and B own 250 of both goods.
A's tastes are captured by the utility function
uA(x1,x2) = x2 + 50lnx1
and B's are captured by the utility function
uB(x1,x2) = x2 + 100lnx1.
a. Let the competitive equilibrium prices be p1 and p2 respectively. Derive both consumersA????1 demand functions for both goods.
ANSWER:
A) These preferences are translog preferences.
Demand functions are given using the equilibrium condition mRS = price ratio
MRS for A= 50/x1= p1/p2
So x1= 50p2/p1
x2= ( M- p1*x1)/p2= (M/p2 )- 50
A sequence of numbers is weakly decreasing when each number in the sequence is the numbers after it. (This implies that a sequence of just one number is weakly decreasing.) Here’s a bogus proof of a very important true fact, every integer greater than 1 is a product of a unique weakly decreasing sequence of primes —a p u sp, for short. Explain what’s bogus about the proof.
Lemma 6.4.1. Every integer greater than 1 is a pusp.
For example, 252 D 7 _ 3 _ 3 _ 2 _ 2, and no other weakly decreasing sequence of
primes will have a product equal to 252.
Bogus proof. We will prove Lemma 6.4.1 by strong induction, letting the induction
hypothesis, P.(n), be n is a pusp:
So Lemma 6.4.1 will follow if we prove that P.(n) holds for all n ≥2.
Base Case (n = 2): P.(2) is true because 2 is prime, and so it is a length one product of primes, and this is obviously the only sequence of primes whose product can equal 2. Inductive step: Suppose that n ≥2 and that i is a pusp for every integer i where 2 ≥ i < n C 1. We must show that P.(n + 1) holds, namely, that n + 1 is also a pusp. We argue by cases: If nC1 is itself prime, then it is the product of a length one sequence consisting of itself. This sequence is unique, since by definition of prime, n C 1 has no other prime factors. So n + 1 is a pusp, that is P.(n + 1) holds in this case. Otherwise, n+1 is not prime, which by definition means n+1 = km for some integers k;m such that 2 _ k;m < nC1. Now by the strong induction hypothesis, we know that k and m are pusps. It follows immediately that by merging the unique prime sequences for k and m, in sorted order, we get a unique weakly decreasing sequence of primes whose product equals n+1. So n+1 is a pusp, in this case as well. So P.(n + 1) holds in any case, which completes the proof by strong induction that P.(n) holds for all n ≥ 2.
Search “scholar.google.com” for a company or school that has defined the role of end-users in the creation of a contingency plan. Discuss why it is (or is not) important to include end users in the process of creating the contingency plan? What are the possible pitfalls of end user inclusion?
– Include at least 250 words in your posting
– Indicate at least one source or reference in your original post
– No plagiarism
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