Many medical professionals believe that eating too much red meat increases the risk of heart disease and cancer. Suppose you would like to conduct a survey to determine the annual consumption of beef by a typical American and want to use four pounds as the desired margin of error for a confidence interval of the population mean. Assume the population standard deviation is 20 pounds. Determine the sample size when:

a)A 90% confidence interval is desired for the mean amount of beef consumed.

b)A 99% confidence interval is desired for the mean amount of beef consumed.

Suppose you want to develop a confidence interval for the proportion of Americans who over-consume red meat with a desire margin of error of 0.1. Determine the sample size needed when:

     c)   A 90% confidence interval is desired for the proportion of Americans who over-consume red meat.

     d)   A 95% confidence interval is desired for the proportion of Americans who over-consume red meat

There has been a lot written about corruption and bribery issues especially in the State of New Jersey.  One recent case involves a Port Authority executive.

Please find some articles regarding corruption and bribery cases and also look up the Port Authority issue.  Post your understanding about the articles you have found and please address your views about how some of the biggest players in a corporation or government entity feel free to abuse the system.

1. 1b There are various items that reduce taxable income relative to total income – what is the general term for these items (collectively, do not list all of them individually)? What do you think is the economic justification for these not being included in taxable income? Pick one and explain its specific justification.
   1. 1c: Under ‘taxable income assessed’ there are various items, usually called ‘amounts’. What is the general term for these items? Pick one, and explain briefly what you think the economic justification for it being included here is.
   2. 1d: Explain the difference between how the items you talked about under (1b) and the items you talked about under (1c) affect:
      1. Your marginal tax rate
      2. Your average tax rate
      3. Total taxes paid

A true breeding red eyed fly with long bristles was crossed to a true breeding white eyed fly with stubble bristles. All F1 progeny are red eyed with stubble bristles. An F1 female is crossed to a tester male and the following numbers of progeny are observed: 56 red eyed, stubble bristles; 72 red eyed, long bristles; 61 white eyed stubble bristles; and 68 white eyed, long bristles. You are asked to perform a chi-squared test for this result.

1. What is the best null hypothesis for this test?

2. What is the expected phenotypic ratio?

3. What is the expected number of individuals in each class?

4. What is the calculated Chi-squared value for independent assortment?

5. If the Chi-squared value had been 0.584 (it's not, by the way.) what is the most accurate conclusion?

Question 3

In a bag of M & M’s there are 80 M & Ms, with 11 red ones, 12 orange ones,
20 blue ones, 11 green ones, 18 yellow ones, and 8 brown ones. They are
mixed up so that each candy piece is equally likely to be selected if we pick
one.
a) If we select one at random, what is the probability that it is red?
b) If we select one at random, what is the probability that it is not blue?
c) If we select one at random, what is the probability that it is red or orange?
d) If we select one at random, then put it back, mix them well and select
another one, what is the probability that both the first and second ones are
blue?
e) If we select one, keep it, and then select a second one, what is the
probability that the first one is red and the second one is green?

This question refers to the Bergson-Samuelson social welfare function

(a) State and explain the conceptual basis of the Bergson-Samuelson social welfare function

(b) Draw a diagram and use it to explain why a Bergson-Samuelson social welfare optimum will be Pareto efficient 6

(c) If an economy is at a Bergson-Samuelson social welfare optimum will there be efficiency in production? Explain

(d) If economic allocations are not Pareto efficient does it make sense to use a Bergson-Samuelson social welfare function to evaluate them? Discuss

1.  Prove that for any graph, the sum the degreesPv∈V deg(v) is twice the number of edges |E|. (By “prove” I mean write a few sentences explaining why it is true.)

2. i) At a recent math seminar, 5 mathematicians greeted each other by shaking hands. Is it possible for each mathematician to shake hands with exactly 3 other people? (No one can shake his or her own hand.) To answer the question, please rephrase the problem as a problem about graphs (is there a graph with 5 vertices ...), state your answer, and then explain why you believe your answer.
ii) Write a conjecture about a more general statement. What do you think happens if we have N mathematicians and we want each to shake the hands of K other people?

3. A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet two inhabitants: Zoey and Mel. Mel says, “At least one of us is a knave,” but Zoey says nothing. Can you determine who is a knight and who is a knave?

Q5:

Global financial markets have exhibited increased volatility this year, with large fall in asset prices followed by large rises.

a) If equities arbitrage with bonds and other assets so, overall, their yields tend to move up and down together, briefly offer an explanation as to why the initial declines in US and Australian equity prices were accompanied by declines in llong maturity bond yields.

b) When pessimism about future yields or borrower defaults sees funds with drawn from equity and bond markets, briefly explain to which asset markets you think portfolio managers retreat.

This all of the question detail

You are interested in knowing whether wealthier people are happier. You collected data from fifty people about their incomes and their overall happiness levels on a scale of 1 to 10. Upon analyzing the results, you find that the correlation coefficient has a value of −0.25. On the basis of this data, respond to the following:

• How would you interpret the correlation coefficient in terms of strength and direction?
• How would the results be affected if you increased the number of subjects in the study to one thousand? Why might that affect the overall correlation?
• How important is it to randomly select subjects? Explain in detail using an example of a sample that might not be truly representative of the population.