Functional Analysis Answers

Assignment Type: Individual Project Deliverable Length: 3-4 page report
Points Possible: 125 Due Date: 3/3/2013 11:59:59 PM CT

How Many People to Survey?
Gallup poll results are prevalent in the media especially leading up to elections as are reports on surveys done by universities and research groups like the Pew Research Center.

The survey results of small groups of people are used to portray a general consensus about a population. Ever wonder how many people should be included in a survey to make it a meaningful reflection of a population? Now you will be able to answer your own question. Be warned; you will never feel the same about these polls and surveys again.

Using the following specific resources, create a lecture (with citations) which includes the following:

Part 1: Survey Analysis

Entertainment Survey
Using a newspaper article from AIU library’s full-text database: National Newspapers (Proquest), create a lecture (with citations) which includes the following:

Describe an entertainment poll or survey. Analyze the number of people who participated in the sample compared to the number in the population. Most news articles will not provide information on the number of people surveyed. In this case critique the validity of the results. (Be sure to cite the article which must be from National Newspapers -ProQuest) Here is a Research Guide.
Discuss how the results of the survey can be used to tell a story or support an idea of the sponsoring company or media group.
Political Survey
Using polls from one of the following sources:

Source 1

Source 2

Describe a political poll or survey. Analyze the number of people who participated in the sample compared to the number in the population.
Discuss how the results of the survey can be used to tell a story or support an idea of the sponsoring company or media group.
General Survey
Using polls from one of the following sources:

Source 1

Source 2

Describe a general opinion poll or survey. Analyze the number of people who participated in the sample compared to the number in the population.
Discuss how the results of the survey can be used to tell a story or support an idea of the sponsoring company or media group.
Overview

Consider the three surveys presented.

Using the knowledge you learned from the textbook, compare and contrast the sample sizes in each of the three surveys mentioned in the post and determine if the samples sizes are appropriate.
In your opinion, which appears to be the most valid? (Cite and reference the textbook)
This section of the paper will be 2-3 pages in length and each survey or poll described MUST come from AIU Library’s National Newspapers- ProQuest Database and Pew Research Center or Gallup.

Please do not use quotes or copy definitions. You will not receive credit for understanding the materials if you use the words of others. Keep in mind that since you did research and you have citations in the body of the post, you must also place a reference list at the end containing the textbook and the articles cited.

Part 2: Application
Create your own 3 question Entertainment or using this General Opinion Survey or another free survey program or this link. Secure a minimum of 20 responses. Your survey respondents may be friends, family or classmates. (NOTE: The small sample size was chosen for convenience and as you know is not a valid sample. The goal is for you to create, deploy and analyze a simple survey.)
Create Excel charts of your results and describe those charts in words. (You will receive no credit for charts that are copied from the survey software.)
Include a copy of your survey
Provide charts of your results and describe those charts in words
Explain how the results of your survey can be used by a media group or company.
This section of the paper will contain 1 page of text and 3 charts.

in the united states 2/5 of them start with M,A,or N how can you use equivelent fractions to find out how many states this is?

what is the largest four digit number,which when divided by 19 leaves a reminder of 7.
here are the option:a.9972 b.9976 c.9978 d.9982

__Unconstrained Function__
F = x₁² + 1/x₁ + x₂ + 1/x₂

Question(a) At x₁ =2 & x₂ = 2, calculate gradient of F.

Question(b) And then, calculate the direction of the deepest descent.

Question(c) Using the direction of the steepest descent from (b), update the design by the standard formula : x¹ = x⁰ + αS¹
Evaluate x₁ , x₂ & F for α=0, 0.2, 0.5, & 1.0 and plot the curve of F versus α.

Question(d) Write the equation for F in terms of α alone. Discuss the character of the function.

Question(e) From (d), calculate dF/dα at α=0.

Question(f) Calculate the scalar product ∇F•S using the results of (a) and (b) and compare this with the result of (e).

integration from 0 to 1
of (m^(m-1)((1-x)^n-1)/ ((a+x)^(m+n)

Suppose the function f is continuous on the interval [a, b] and never zero on [a, b].
Is it possible that f(z) < 0 for some z ∈ [a, b] and f(w) > 0 for some w ∈ [a, b]?
Explain your answer.

Suppose f is a function such that
f(x) = x^2 x element Q,
0 x element R − Q.
Is f continuous at c = 0? Is f differentiable at c = 0?

prove that two norm linear spaces may be topological isomorphic but not necessary congruent give example.