Tag: Mathematics

Product 1: Data Analysis Strategy Paper and SPSS Output[5 points]

The first product is a maximum 1-page description of the “Data Analysis Strategy” for your study that includes the following information:

• Briefly (2 or 3 sentences) describe the source of the data for this study (i.e., the GSS 2018 – a brief note about the methodology of the GSS, cited in APA format. Note: You can find the proper citation for the GSS data in the Codebook).
• If you used a subset of the sample for your study, note that in this paper (e.g., if you selected only the females in the sample).
• Identify and provide your rationale for the type of statistical analyses used to test the 3 hypotheses.
• State the alpha level for the three hypothesis tests.
• If you decided to recode or newly compute any variables differently than in step 2, explain why and how you have chosen to construct the “new variable,” including providing a frequency distribution table with the recoded variables’ values.
• Outcome Evaluation for Future Study: Based on the findings of your research study, briefly pose an intervention or program that you could research in a future study. It doesn’t have to flow directly from your findings in your current study. You could take the research in a different direction (e.g. a different study population – you don’t have to use the GSS data – you could use any primary or secondary data you wanted). You must include TWO specific outcomes that you would hope to see from this program or intervention. And you must specify how you would MEASURE these two outcomes.
• Insert your SPSS output for your statistical tests and any other relevant output generated for your data analysis into the end of this paper.

For example: Let’s say your current study was about job-related factors that were related to discrimination or harassment in the workplace. For a future study to expand on this, you might look at job related discrimination or harassment in LGBTQ service workers. You might propose the creation of a workplace education program with a goal of increasing knowledge and tolerance of diverse gender identities. You would want to measure whether this workplace education program “worked” (was “successful”) to increase knowledge and tolerance of gender diversity. You might propose a pre-post survey for people taking this educational workshop, where they would be asked about their knowledge and attitudes toward gender diversity before and after the workshop. Your two outcome measures would be knowledge of and attitudes toward gender diversity.

You will be graded on a clear and succinct explanation of your study methodology, data analysis and future study outcome measurement as outlined above.

Product 2: Research Poster Suitable for Presentation at a Conference [25 points]

Please use the poster template provided on Blackboard to create your poster. You will be graded on each section of the poster for succinct, clear, and accurate information, based on the correct interpretation of the statistical tests and ability to “translate” these findings into narrative and table format; clear and professional formatting; and clear and informative tables which should include vital information such as titles, headings, subheadings, test statistics, sample sizes (n), and p levels. Strive to place your findings from your 3 hypotheses in a single table (but hopefully no more than two tables).

NOTE: You CANNOT simply cut and paste your SPSS output into the Poster Template. Attached are the hypothesis that are used for this paper and work for poster: Research Hypotheses

This research will test three hypotheses to test the influence of religion on the attitude towards suicide. The data being used in testing the hypothesis was obtained from the GSS 2018 data. The hypothesis to be tested include;

Hypothesis 1
Null Hypothesis (Ho)	Religious affiliation does not affect attitudes/behaviors regarding suicide
Alternative Hypothesis (Ha)	Religious affiliation does affect attitudes/behaviors regarding suicide
Directional or Non-directional?	Non-directional
Independent Variable Name (IV) – the variable name in the GSS	Religion and Spirituality
IV Description (from Codebook)	RELITEN
IV Level of Measurement (N,O,I,R)	Ordinal
IV Answer categories (can be copied directly from Codebook)	Strength of affiliation Valid Values 1 STRONG 2 NOT VERY STRONG 3 SOMEWHAT STRONG 4 NO RELIGION Missing Values 0 IAP 8 DK 9 NA
Do you plan to recode this variable?	No/maybe
Dependent Variable Name (DV) – the variable name in the GSS	Attitude toward: Suicide in case of an incurable disease
DV Description (from Codebook)	SUICIDE1
DV Level of Measurement (N,O,I,R)	nominal
DV Answer categories (copied from the Codebook)	Standard Attributes Label Suicide if incurable disease Valid Values 1 YES 2 NO Missing Values 0 IAP 8 DK 9 NA
Do you plan to recode this variable?	No/maybe[MW1]

Hypothesis 2
Null Hypothesis (Ho)	There is no connection between attitudes about suicide and type of religion
Alternative Hypothesis (Ha)	There is a connection between attitudes about suicide and type of religion
Directional or Non-directional?	Non-directional
Independent Variable Name (IV) – the variable name in the GSS	Religion and Spirituality
IV Description (from Codebook)	RELIG
IV Level of Measurement (N,O,I,R)	nominal
IV Answer categories (can be copied directly from Codebook)	Label R’s religious preference Valid Values 1 PROTESTANT 2 CATHOLIC 3 JEWISH 4 NONE 5 OTHER 6 BUDDHISM 7 HINDUISM 8 OTHER EASTERN 9 MOSLEM/ISLAM 10 ORTHODOX-CHRISTIAN 11 CHRISTIAN 12 NATIVE AMERICAN 13 INTER-NONDENOMINATIONAL Missing Values 0 IAP 98 DK 99 NA
Do you plan to recode this variable?	YES
Dependent Variable Name (DV) – the variable name in the GSS	Attitude toward: Suicide general
DV Description (from Codebook)	SUICIDE4
DV Level of Measurement (N,O,I,R)	Nominal
DV Answer categories (copied from the Codebook)	Label Suicide if tired of living Valid Values 1 YES 2 NO Missing Values 0 IAP 8 DK 9 NA
Do you plan to recode this variable?	No

Hypothesis 3
Null Hypothesis (Ho)	Belief in the Bible does not affect attitudes towards suicide
Alternative Hypothesis (Ha)	Belief in the Bible has effects on one’s attitude towards suicide
Directional or Non-directional?	Non-directional
Independent Variable Name (IV) – the variable name in the GSS	Religion and Spirituality
IV Description (from Codebook)	BIBLE
IV Level of Measurement (N,O,I,R)	nominal
IV Answer categories (can be copied directly from Codebook)	Label Feelings about the Bible Valid Values 1 WORD OF GOD 2 INSPIRED WORD 3 BOOK OF FABLES 4 OTHER Missing Values 0 IAP 8 DK 9 NA
Do you plan to recode this variable?	no
Dependent Variable Name (DV) – the variable name in the GSS	Attitude toward: Suicide general
DV Description (from Codebook)	Suicide3
DV Level of Measurement (N,O,I,R)	Nominal
DV Answer categories (copied from the Codebook)	Suicide 2: Label Suicide if bankrupt Valid Values 1 YES 2 NO Missing Values 0 IAP 8 DK 9 NA
Do you plan to recode this variable?	No

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test to be used in SPSS are chi square and cross tabulation will attached poster to be used

I don’t understand this Discrete Math question and need help to study.

 

A mathematical proof is an argument that convinces other people that something is true. In mathematical logic, “likely to be true” is not good enough. We try to prove things beyond any doubt at all.

 

• Compare proof by contradiction and proof by contrapositive and provide an example of one or the other.

Solve these for me please and show the explanations. Thank you so much.

1- Use the method of undetermined coefficients to find one solution of: y”- y’- y = 2e^(2t)

y(t) = ?

2- Find the solution of y”+7y’ = 392 sin(7t) + 392 cos(7t)

with y(0) = 2 and y'(0) = 9

y = ?

I will give you all the homework and solution.

This exam will not use R.

course introduction: An introduction to univariate time series models and associated methods of data analysis and inference in the time domain and frequency domain. Topics include: auto regressive (AR), moving average (MA), ARMA and ARIMA processes, stationary and non-stationary processes, seasonal ARIMA processes, auto-correlation and partial auto-correlation functions, identification of models, estimation of parameters, diagnostic checking of fitted models, forecasting, spectral density function, periodogram and discrete Fournier transform, linear filters, parametric spectral estimation, dynamic Fournier analysis. Additional topics may include wavelets and long memory processes (FARIMA) and GARCH Models. The use of statistical software, such as JMP, or R, is fully integrated into the course.

7.5-1. Let Y1 < Y2 < Y3 < Y4 < Y5 < Y6 be the order statistics of a random sample of size n = 6 from a distri-bution of the continuous type having (100p)th percentile πp. Compute

(a) P(Y2 <π0.5 < Y5). (b) P(Y1 <π0.25 < Y4). (c) P(Y4 <π0.9 < Y6).

7.5-4. Let m denote the median weight of “80-pound” bags of water softener pellets. Use the following random sample of n = 14 weights to find an approximate 95% confidence interval for m:

80.51 80.28 80.40 80.35 80.38 80.28 80.27 80.16 80.59 80.56 80.32 80.27 80.53 80.32

(a) Find a 94.26% confidence interval for m.

(b) The interval (y6, y12) could serve as a confidence inter-val for π0.6. What is its confidence coefficient?

7.5-5. A biologist who studies spiders selected a random sample of 20 male green lynx spiders (a spider that does not weave a web, but chases and leaps on its prey) and measured the lengths (in millimeters) of one of the front legs of the 20 spiders. Use the following measurements toconstruct a confidence interval for m that has a confidence coefficient about equal to 0.95:

15.10 16.40 13.55 15.75

13.60 16.45 14.05 17.05 15.25

17.75 15.40 16.80

20.00 15.45 16.95 19.05 16.65 16.25 17.55 19.05

7.5-12. Let Y1 < Y2 < ··· < Y8 be the order statistics of eight independent observations from a continuous-type distribution with 70th percentile π0.7 = 27.3.(a) Determine P(Y7 < 27.3). (b) Find P(Y5 < 27.3 < Y8).

8.1-2. Assume that the weight of cereal in a “12.6-ounce box” is N(μ, 0.22). The Food and Drug Association (FDA) allows only a small percentage of boxes to contain less than 12.6 ounces. We shall test the null hypothesis H0: μ = 13 against the alternative hypothesis H1: μ< 13. (a) Use a random sample of n = 25 to define the test statistic and the critical region that has a significance level of α = 0.025.

(b) If x = 12.9, what is your conclusion? (c) What is the p-value of this test?

8.1-3. Let X equal the Brinell hardness measurement of ductile iron subcritically annealed. Assume that the distri-bution of X is N(μ, 100). We shall test the null hypothesis H0: μ = 170 against the alternative hypothesis H1: μ> 170, using n = 25 observations of X.

(a) Define the test statistic and a critical region that has a significance level of α = 0.05. Sketch a figure showing this critical region.

(b) A random sample of n = 25 observations ofX yielded the following measurements:

170 167 174 179 179 156 163 156 187 156 183 179 174 179 170 156 187 179 183 174 187 167 159 170 179

Calculate the value of the test statistic and state your conclusion clearly.

(c) Give the approximate p-value of this test.

1. Let A ⊆ R. We say that an element c ∈ A is isolated if there is an ε > 0 such that
A ∩ (c − ε, c + ε) = {c}.
(a) Show that c ∈ A is an isolated point if and only if it is not a limit point of A.
(b) Show that every function f : A → R is continuous at each isolated c ∈ A.
(c) Show that every function f : Z → R is continuous on its domain Z.

2. For each of the following functions f : A → R, find f(A) and hence decide whether f
(equivalently its range) has an upper bound, a lower bound, a maximum or a minimum.
(a) f(x) = x
3
, A = (−3, 2).
(b) f(x) = x
2
, A = (−3, 2)
(c) f(x) = (
x if x ∈ Q
0 if x /∈ Q
, A = [0, a] where a > 0.

3. Assume f : R → R is continuous on R and let K = {x : f(x) = 0}. Show that K is a
closed set.

4. Give an example of each of the following, or state that such a request is impossible. For
any that are impossible, supply a short explanation for why this is the case.
(a) A continuous function f : (0, 1) → R and a Cauchy sequence (xn) in (0, 1) such
that (f(xn)) is not a Cauchy sequence.
(b) A continuous function f : [0, 1] → R and a Cauchy sequence (xn) in [0, 1] such that
(f(xn)) is not a Cauchy sequence.
(c) A continuous function f : [0, 1] → R which has a maximum but no minimum.
(d) A continuous bounded function f : (0, 1) → R that attains a maximum value but
not a minimum value.

5. (a) Let f be a continuous real-valued function with domain (a, b). Show that if f(x) = 0
for each rational number x in (a, b), then f(x) = 0 for all x ∈ (a, b).
(b) If f and g are continuous real-valued functions with domain (a, b) and f(x) = g(x)
for all rational x ∈ (a, b), must f and g be the same function?

1. Descriptive Statistics: In six sentences or more, explain how you would use the descriptive statistical procedure(s) at work or in your personal life.
2. Misuse of Statistics: As we will see in the next 12 weeks, statistics when used correctly can be a very powerful tool in managerial decision making.

   Statistical techniques are used extensively by marketing, accounting, quality control, consumers, professional sports people, hospital administrators, educators, politicians, physicians, etc…

   As such a strong tool, statistics is often misused. Everyone has heard the joke (?) about the statistician who drowned in a river with an average depth of 3 feet or the person who boarded a plane with a bomb because “the odds of two bombs on the same plane are lower than one in one millionth”.

   Can you find examples in the popular press of misuse of statistics?

3. How to Display Data Badly : Read the article “How to Display Data Badly” by Howard Wainer. It is attached here: How to Display Data Badly and also posted under the Content tab (after you choose the Content tab, choose Course Content and Session 1 from the list on the left).

   Next read, Chart Junk Considered Useful after All, by Robert Kosara, https://eagereyes.org/criticism/chart-junk-considered-useful-after-all

   In your own words, describe “Chart Junk”.

   When should Chart Junk be avoided. When is it useful?

   Include an image or link to an example of the worst data display you have seen at work or in the media (not in Wainer’s article).

   Wainer gives rules for how to make bad charts & graphs. Which of Wainer’s rules describes what’s so bad about your example?

4. Discussion: Simpson’s Paradox : A family member can go to one of two local hospitals for heart surgery.

   Checking the history for the past year, you find that each of the two hospitals has performed cardiac surgery on 1000 patients. In hospital A 710 patients survived (71%). In hospital B 540 (54%) survived.

   Based on the numbers presented, which hospital do you think is superior in cardiac surgery?

   Surely hospital A is better, right?

   Now, let’s look at more data. The below chart summarizes three categories of patients (those entering in fair, serious and critical condition) and the survival rate from surgery (in percent) for the two local hospitals.

Patient Entering Condition	Hospital A	Hospital B	Survivors from A (# and percent)	Survivors from B (# and percent)
Fair	700	100	600 or 86%	90 or 90%
Serious	200	200	100 or 50%	150 or 75%
Critical	100	700	10 or 10%	300 or 43%
Total	1000	1000	710 or 71%	540 or 54%

Looking at the data broken down in this way, we see that Hospital B has a higher success rate in all three categories of patients but when averaged all together, Hospital A has the higher overall survival rate. Based on the numbers presented, which hospital do you think is superior in cardiac surgery?

Exercise 1

Consider the dierential equation

_ = (

p

2

2

cos )( cos )

on the circle, where is a real parameter.

(a) Compute all bifurcation points (; ):

(b) Draw all qualitatively dierent phase portraits on the circle.

(You do not need to draw the bifurcation diagram.)

(c) What types of bifurcations occur at the bifurcation points?

Exercise 2

(a) Classify the xed point at the origin and draw the phase portrait of the dierential

equation

x_ = 2x y;

y_ = y:

(b) Determine all a 2 R so that the dierential equation

x_ = (1 + 4a)x 5ay;

y_ = ax y

has a stable spiral at the origin.

(c) Determine all a 2 R so that the dierential equation

x_ = a2(a + 2)x;

y_ = 3x + (a 2)a(a + 1)y

has a Lyapunov stable xed point at the origin.

Exercise 3

A model for the population sizes of A, B 0 is given by

dA

dt

= r1A k1AB;

dB

dt

= r2B k2AB;

where r1; r2; k1; k2 > 0 are constants.

(a) By rescaling A;B and t, derive the following non-dimensionalized version of the

model

dx

d

= x(1 y);

dy

d

= y( x):

(b) Sketch the nullclines for the non-dimensionalized model, including the vector eld

along the nullclines.

(c) Based on the nullclines, sketch a plausible phase portrait.

Exercise 4

Consider the dierential equation

x_ = r x(2×2 + 3x 12):

It undergoes saddle-node bifurcations at (r; x) = ( 8; 1); (20; 2) and there are

no other bifurcations. The corresponding bifurcation diagram, with all xed points

plotted in blue, is

Let x(t) be the solution with x(0) = 4 for r = 0: Explain what happens to x(t)

as …

(a) … r is increased continuously to r = 30 and then lowered back to r = 0:

(b) … r is increased continuously to r = 30, then decreased to r = 10; and nally

increased back to r = 0:

Remark. You may answer the question in words and/or with diagrams. No computa-

tions necessary.

Exercise 5

Consider the dierential equation

x_ = 2x 3y y3;

y_ = 12x + 2y y5:

(a) Show that the origin is the unique xed point.

(b) Classify the xed point using the linearization.

What can you deduce about the stability of the xed point and the phase portrait

of the non-linear system near the xed point?

(c) Draw a qualitative phase portrait for the non-linear system. Indicate the stable

and unstable manifolds.

Conduct an analysis and hypothesis test of your choice on the data you collected. Write a 250-500 word research summary of the findings generated in the assignments for Topics 2 through 5. The research summary should address the following.

• Explain what type of analysis and hypothesis test was conducted on the data collected.
• Summarize the survey results based on the results of the data you analyzed.
• Include the Excel analysis as part of the document.

APA format is not required, but solid academic writing is expected.

This assignment uses a rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion.

Summary as a word document, and the final hypothesis test in excel.