After watching the following clip, discuss why the cones topple and dump the water after the water in the cones reach a certain level. Discuss i) why the the cones remain in equilibrium before toppling, ii) what disrupted the equilibrium condition later.

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Water bucket damper at splash pad

 

 

After watching the following clip, discuss why the cones topple and dump the water after the water in the cones reach a certain level.

Discuss

i) why the the cones remain in equilibrium before toppling,

ii) what disrupted the equilibrium condition later.

The answers to the above questions must be supported with relevant sketches, free body diagrams, and static equilibrium equations

How many individuals are included in the data set? Is the left-right ideology similar on average for those who did and not answer the item NatFrEst? Calculate the median of the variable NatFrEst. What does this tell us about the distribution of perceptions about fraudulent benefits claims?

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Final Coursework

Quantitative Data Analysis (POLS0083)

Instructions

• The final assessment will be posted on Moodle on 17th December 2021 at 6pm, and is due on 10th January 2022 at 2pm. Follow all designated SPP submission guidelines for online submission as detailed on the POLS0083 Moodle page. Standard late submission penalties apply.

• This is an assessed piece of coursework (worth 70% of your final module mark) for the POLS0083 module; collaboration and/or discussion of the coursework with anyone is strictly prohibited. The rules for plagiarism apply and any cases of suspected plagiarism of published work or the work of classmates will be taken seriously.

• As this is an assessed piece of work, you may not email/ask the course teaching team questions about the coursework.

• Along with the coursework questions, the necessary data sets for the coursework can be found on the POLS0083 page on Moodle.

• The coursework should be submitted via the ‘POLS0083 – 2,000 word Final (70%)’ link on the course Moodle page. You will need to click the ‘Submit Paper’ link at the bottom of the page. When presented with the ‘Submit Paper’ box, the ‘Submission Title’ should be your candidate number, and you should upload your document into the box provided. Remember to state ONLY your candidate number on your coursework (your candidate number is made up of four letters and one number e.g. ABCD5). Your name and/or student number MUST NOT appear on your submission.

• The coursework consists of three separate sections, each with several questions. The marks allocated for each section are indicated in the text. You must complete each question to achieve full marks.

• Unless otherwise stated, answers should be written in complete sentences. Be sure to answer all parts of the questions posed and provide a substantive interpretation of the results.

• The word count for this assessment is 2,000 words. This does not include the code, your output, or any words (or numbers) contained within tables or figures.

• Submit your type-written (numbered) answers in a single document (a word file or a pdf file). You can, but do not have to, use RMarkdown to produce such a file. If you use RMarkdown, you can integrate the code with the answers (make sure that it is completely visible). If you do not use RMarkdown, you can create an appendix section at the end which contains all the R code needed to reproduce your results. Your code has to work when we run it. You do not need to include the code that failed to run, but just the well-annotated, cleaned-up version. If you do not provide the code to a
question, any written answer to that question will be disregarded.

• You may assume the methods you have used (e.g. difference in means, linear regression, etc) are understood by the reader and do not need definitions, but you do need to be able to explain what they do and how they apply to answering the question.

• Round all numbers to two digits after the decimal point.

• Do not screenshot or copy and paste any brute R output (e.g. lm(y ∼ x)) into your answers. Create a formatted table that is easy to read.

• Assign every table and figure a title and a number and refer to the number in the text when discussing a specific figure or table

Section 1
Public perceptions of benefit fraud
Trust in social welfare institutions relies on how the public perceives of the deservingness of recipients of such benefits. In particular, notions of so-called ‘benefit cheats’ erodes public confidence in social welfare. Past surveys have shown that the public tend to greatly over-estimate the financial scale of benefit fraud. For example, a 2013 Ipsos MORI study found that on average, respondents guessed that £24 out of every £100 in benefit claims is done fraudulently, whereas the official estimate is around £0.70 of every £100.

In this section, we explore public perceptions about fraudulently claiming benefits, and in particular, about how widespread false benefits claims are. More specifically, we will examine whether certain socio-demographic characteristics are associated with public perceptions about how widely false benefit claims are made in the UK.
We will use part of the British Social Attitudes (BSA) data set on poverty and wealth, which you can download as bsa-poverty.csv from the POLS0083 Moodle page. The data set contains the following variables:

Variable name Description

NatFrEst Answer to the question “Out of every 100 people receiving benefits in Britain, how many have broken the law by giving false information to support their claim?”

leftrigh Five-point left-right ideological scale, with 0 to the left and 4 to the right RSex Sex of respondent, 1 if male or 0 if female HEdQual3 Completed university degree, 1 if the respondent completed degree or 0 if not

You can load the data set by using the following command: bsa <- read.csv(“data/bsa-poverty.csv”)

Questions (42 Marks)
1. How many individuals are included in the data set?

2. Is the left-right ideology similar on average for those who did and not answer the item NatFrEst?

3. Calculate the median of the variable NatFrEst. What does this tell us about the distribution of perceptions about fraudulent benefits claims?

4. Create a histogram for NatFrEst and interpret it. What does this tell us about public perceptions about fraudulent benefits claims?

5. We are interested in seeing whether there is a relationship between a person’s left-right orientation and how widespread they think fraudulent benefit claims are. Fit the relevant simple linear regression model and interpret the substantive significance of the estimated slope coefficient. You do not need to discuss statistical significance.

6. State a null and an alternative hypothesis for the estimated slope coefficient, decide whether to reject the null hypothesis, and provide a conclusion.

7. How is your conclusion in Question 6 related to Type I and Type II error?

8. We now add whether the respondent completed a university degree and respondent sex to our analysis. Interpret the estimated coefficient for the left-right orientation. Does your answer to the question about the relationship between a person’s left-right orientation and NatFrEst change? If so, how?

9. Calculate and interpret the 99% confidence interval for the estimated coefficient for completing a university degree from the model you fitted in Question 8. What does the estimated standard error tell us?

10. Finally, we are interested in whether the relationship between left-right orientation and perceptions of how widespread benefit fraud is also depends on an individual’s education level.
a. Add the relevant interaction term to your regression model and display your results.
b. Assess the model fit for this regression model.
c. Interpret the estimated interaction term and discuss its substantive and statistical significance.
d. Interpret the intercept and its statistical significance. Is the intercept meaningful in this regression model?
e. Visually represent the results from the regression model using four lines (one each for male respondents with a university degree, female respondents with a university degree, male respondents without a university degree and female respondents without a university degree) and describe what your graph shows.

Section 2

Dystopian fiction and willingness to justify radical political action

We now look at part of the recent study by Jones and Paris (2018), who conducted a series of survey experiments to examine whether exposure to dystopian fiction affects an individual’s political beliefs. They define dystopian fiction as “portray[ing] a dark and disturbing world dominated by an overwhelmingly powerful. . . controlling entity that acts to undermine core values”. In particular, the authors hypothesised that exposure to dystopian fiction would lead to higher support for more radical political action, especially for more violent action.
In the first study, the authors randomly assigned the US-based respondents into two groups. Respondents assigned to the treatment group first read an excerpt from the first book in Hunger Games, and then watched a 17-minute video with various violent scenes from the Hunger Games films. Respondents assigned to the control group were not exposed to any media.
The premise of Hunger Games is that an overwhelmingly powerful government forces individuals to take part in a contest where the participants are forced to kill each other until only one survivor remains.
The outcome variables are a series of attitudinal items about willingness to justify different disruptive activities: civil disobedience, damaging government property, cyber attacks on government websites, armed rebellion, and violent protest.

The data file you will use, which can be downloaded on the POLS0083 Moodle page, is titled dystopia.csv.
The data includes the following variables:
Variable name Description hgindic Treatment group, with 1 for those exposed to Hunger Games and 0 for the
control group
j_disobed How much civil disobedience can be justified, on a 0-1 scale
j_damage How much damaging government property can be justified, on a 0-1 scale
j_cyber How much cyberattacks on government websites can be justified, on a 0-1 scale
j_rebel How much armed rebellion can be justified, on a 0-1 scale
j_violent How much violent protest can be justified, on a 0-1 scale
female Respondent sex, with 1 as female and 0 as male ideo Respondent left-right ideological orientation, with higher scores indicating the right, on a 1-6 scale
You can load the data set by using the following command: dystopia <- read.csv(“data/dystopia.csv”)

Questions (33 Marks)
1. What are the proportions of female respondents within the treatment and control groups?
2. We are interested in the outcome variables for civil disobedience and armed rebellion. For each of these outcome variables:
a. Create a boxplot for each treatment group and interpret the results.
b. Calculate difference in means by treatment group and interpret the results. You do not need to discuss statistical significance.
c. Conduct the appropriate hypothesis test and interpret the results for the difference in means.

3. In the current study, in which two ways can we understand the population from which the sample is drawn?

4. With what assumptions can we interpret the results from Question 2 as causal?
5. Fit a regression model for each outcome variable with the treatment group, sex, and ideology. Does the estimated difference in means change? What does this tell us about the randomisation of treatment in this study?
6. Do your results support the authors’ hypothesis about the link between dystopian fiction and willingness to support radical political action? State your conclusions in terms of substantial and statistical significance.

Section 3

Direct democracy and citizens’ local support
Does direct democracy (such as local referendums) increase satisfaction with local policies and governmental institutions? Marien and Kern (2018) explore this question in their article “The Winner Takes It All:
Revisiting the Effect of Direct Democracy on Citizens’ Political Support”.
Drawing on the existing literature, the authors argue that direct democratic instruments have short-term
positive effects on satisfaction with local policies and institutions, since they increase the perceived fairness of
decision-making and ability to influence political outcomes among the electorate.
To test their hypothesis, the authors conducted multiple surveys during the spring of 2015, when the
Belgian city Mechelen conducted a referendum on traffic circulation, after citizens had objected to the local
government’s initial plans. The researchers collected survey data before and after the referendum took place
both from a sample of local residents in Mechelen who lived in neighbourhoods affected by the traffic diversion
plans (treatment group) and from a sample of residents of a similar neighbourhood in Mechelen not affected
by the traffic circulation plans (control group).

The data file you will use, which can be downloaded on the POLS0083 Moodle page, is titled referendum.csv.

The data includes the following variables:
Variable name Description
idresp Respondent ID
neighb Neighbourhood, 1 as the treatment group and 0 as the control
w1_byear Respondent birth year
primary Highest level of education completed – primary – with 1 Yes and 0 No
secondary Highest level of education completed – secondary – with 1 Yes and 0 No
tertiary Highest level of education completed – tertiary – with 1 Yes and 0 No
w1_trust_general General level of trust on a 0-10 scale, with higher scores meaning more trust, before the referendum
w1_pol_interest Political interest on a 0-10 scale, with higher scores meaning more interest, before the referendum
w1_democracy_satis Democratic satisfaction on a 0-10 scale, before the referendum, with higher scores meaning higher satisfaction
w2_democracy_satis Democratic satisfaction on a 0-10 scale, after the referendum, with higher scores meaning higher satisfaction
You can load the data set by using the following command: referendum <- read.csv(“data/referendum.csv”)

Questions (25 Marks)
1. Is the average level of democratic satisfaction before the referendum significantly different (statistically and substantively) between respondents in the treatment and control groups?

2. Provide some evidence that the treatment and control neighborhoods are similar in terms of respondent characteristics before the referendum took place.

3. Focusing on the respondents living in a neighborhood affected by the government’s plan on traffic circulation, use a before-after design to estimate the average treatment effect. Is this difference significant both statistically and substatively?
4. With what assumptions can we consider the results of Question 3 as causal?

5. Calculate and interpret the difference-in-differences for democratic satisfaction for the two neighborhoods and interpret your results.

6. Do the results in Question 5 support the authors’ hypothesis about the link between direct democracy and citizens’ perceptions about democracy? Why or why not?

7. With what assumptions can we consider the results of Question 6 as causal?

Obtain the matrix that represents spin squared, IS2], and show it commutes with IS,I, [Sy] and [S,I. What is the significance of this result?

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Math/Physic/Economic/Statistic Problems

The operator for the square of orbital angular momenturn, 1,2, has eigenfunctions and eigenvalues:

L2 Km(0, = 1(1 + 1),0 (0,)with / = 0,1,2 …

where Yin,(0, 0) are the spherical harmonic functions.

a) Obtain the energy eigenvalues and eigenfunctions associated with the rotational motion of rigid diatomic molecules in terms of the rnoment of inertia of the molecule.

b) The presence of molecules in interstellar space canb detected using microwave spectroscopy. The detected microwave radiation is associated with the spontaneous transition of molecules frorn their first excited rotational state to their ground state. At what frequency would radiation emitted from SO molecules be detected.

You may assume the separation of the S and 0 atoms is d=1.48×10-1.rn and the atornic rnasses are 32 amu for S and 16 amu for 0, the moment of inertia of a rigid dimer is given as

In the matrix representation of intrinsic spin the cartesian components of angular momenturn are represented by the Pauli spin matrices given as:
= 10) [s,]=(° Pi) IS = (0 21)

c) Obtain the matrix that represents spin squared, IS2], and show it commutes with IS,I, [Sy] and [S,I. What is the significance of this result?

d) The general quanturn spin state of an electron is written as a vector (;). Three successive measurements of S,, Sy and S, are made and a positive answer obtained in each case. What are the spin states after each measurement?

e) A final measurement is then made of Sr, what are the possible outcomes of this measurement and discuss how the predictions differ from classical physics.

Prove that the invariant measure of the chaos generated by the map f (x) is μ(x) ≡ 1,and convincingly prove that the Lyapunov exponent is λ = −a ln(a) − (1 − a) ln(1 − a)

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Math/Physic/Economic/Statistic Problems

1. Consider the system
(xn+1 yn+1)= L(f (xn)f (yn), with L =[1 − ǫ ǫǫ 1 − ǫ]
. (1) and f (x) ={x/a, 0 ≤ x ≤ a(1 − x)/(1 − a), a < x ≤ 1. (2)

Prove that the invariant measure of the chaos generated by the map f (x) is μ(x) ≡ 1,and convincingly prove that the Lyapunov exponent is λ = −a ln(a) − (1 − a) ln(1 − a)

2. Now iterate this system on the computer for a = 0.7 and ǫ = 0.2, which is below the critical coupling strength ǫc. Show a picture of the outbreaks. Sometimes, for some of you, the system can accidentally get stuck into the synchronized state, which it never leaves. Why ? Think about numerical precision. 1 2

3. Avoid this being trapped inside the computer by taking the parameters a slightly different for the two coupled maps. Compute the histogram of outbreaks P (z), z =ln |(xn − yn)/2|, and verify its exponential behavior, P (z) ∝ exp(κz). As explained in the lecture notes, κ should be proportional to the transverse Lyapunov exponent λ⊥
(for which an analytical expression exists: Eq.8.4 of the lecture notes). You will report on this proportionality by running the systems for various coupling strengths, both below and above criticality. The proportionality factor involves the second (curvature) moment of the distribution of the finite-time Lyapunov exponents λ of the individual
system. You can either compute the analytic form (Eq.8.14 of the lecture notes), or find it from simulating the (single) map and looking at the distribution of λ. You must try very hard to verify this relation.
Maps are quick, but it is interesting to see this theory work for differential equations. It also provides confidence in handling continuous-time systems through integration of coupled ordinary differential equations. You will find that the phenomenology is exactly the same, so, if you understood the previous questions, you will know exactly what to do in the ODE system.
d2θmdt2 + γ dθmdt + sin θm = Γ0 cos(Ωt) + c(sin θm − sin θs)/2 (3)
d2θsdt2 + γ dθsdt + sin θs = Γ0 cos(Ωt) + c(sin θs − sin θm)/2 (4)
with damping γ = 0.2, Γ0 = 1.2 and Ω = 0.5. It is the synchronization of symmetrically coupled driven pendula. It so happens (which you may verify) that the critical coupling strength ccr = 0.7948 . . ..

4. Compute the histogram of the difference between slave and master, z(t) = ln({(θs −θm)2 + ( ̇θs − ̇θm)2}1/2) slightly below criticality (ccr = 0.7948). Avoid the “getting stuck” pitfall. Show a picture of the histogram. Also realize that θ and θ + 2π are exactly the same state.

5. Now we must verify from the value of the transverse Lyapunov exponent λ⊥ that the number above is indeed the critical coupling strength. Compute λ⊥ and show that it changes sign if we move through ccr. See the section “how to compute Lyapunov exponents”.
First prove that the transverse dynamics δ⊥ = θm − θs satisfies the linear equation
̈δ⊥ + γ ̇δ⊥ + (1 − c)δ⊥ cos θ(t) = 0,
1This has resulted in great confusion in the literature, see the remarkable paper Reconsideration of intermittent synchronization in coupled chaotic pendula, by S. Rim et al., Phys. Rev. E 64, 060101(R) (2001). See also the references at the end of Chapter VIII of the lecture notes. The articles are on Brightspace.
2MATLAB has an option to compute with more than 16 digits, but this has little to do with physics with driving force cos θ(t) from the synchronized state. Add this ODE to your system of ODE’s (see the last page of this assignment) and use it to compute the Lyapunov exponent λ⊥.
In order to evade the locking pitfall, you should add noise. For example, uniformly distributed random numbers on the interval [−5 × 10−11, 5 × 10−11] to θm and θs after each 10 integration steps (0.1 s). Of course this implies that z can never become smaller than ≈ 10−10. In this sense, synchronization is the ability of the coupled systems to overcome tiny noise that tries to push them apart while it is amplified by their positive Lyapunov exponent.

6. Finally, establish the relation between the “shape” κ of the histogram of outbreaks and λ⊥.
Do the same as in (3), i.e. relate the proportionality factor between κ and λ⊥ to the width of to the Gaussian distribution of long-time Lyapunov exponents ΛT . This is an “open problem”, you can go as far as you like. Ultimately you would like to see the same relation between the statistics of the outbreaks, the value of the transverse Lyapunov exponents, and the statistics of the instantaneous “Lyapunov exponents” of the synchronized system as in the coupled map case. Lyapunov exponents.

What is the standard error of measurement? What is the standard error of the mean? Discuss the term confidence interval. What are four main assumptions for parametric statistics? Discuss and explain in your own words each of the four main assumptions.

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Math/Physic/Economic/Statistic Problems

 

Question 1. Inferential Statistics Concepts and Assumptions & Concepts

A. What is the standard error of measurement?

B. What is the standard error of the mean?

C. Discuss the term confidence interval.

D. What are four main assumptions for parametric statistics?

E. Discuss and explain in your own words each of the four main assumptions.

F. Why it is important to discuss or test the assumptions before conducting parametric statistical analyses?

Question II. Standard Error of the Mean and Confidence Intervals

A district-wide test is used to measure math aptitude in freshmen in high school students, with a mean of 78 and a standard deviation of 12. Thirty-six selected freshmen took the test, and their mean score was 85. You are tasked to examine if these students are significantly different from the district test group.

A. Calculate the standard error of the mean (SEM)? (Note: SEM is calculated by dividing the standard deviation by the square root of the sample size.)

B. Why is it better to use a 99% CI then a 95% CI?

C. Explain a 95% CI and give an example or apply the meaning in a real-world situation (you do not need to calculate by hand but can if you want to! OR you could create a fake dataset on SPSS and have SPSS calculate the CI, OR make it up OR use an online CI calculator such as The point of this assignment question is for you to understand what the 95% CI means.

D. Explain a 99% CI and give an example or apply the meaning in a real-world situation (you do not need to calculate by hand but can if you want to! OR you could create a fake dataset on SPSS and have SPSS calculate the CI, OR make it up OR use an online CI calculator such as The point of this assignment question is for you to understand what the 99% CI means.

Question III. Testing for Parametric Assumptions

A movie company wants to test if there are movies that are preferred more by females and preferred more by males. The movie company surveyed 20 men and 20 women and showed half of each sample a film that was supposed to be a movie preferred more by females (The Notebook) and males (The Godfather). In all cases, the movie company measured their excitement as an indicator of how much they enjoyed the film. Open the movie SPSS file, and answer the following questions:

A. Conduct the required analyses to test for the assumptions of normality (Shapiro-Wilks or Kolmogorov- Smirnov) and homogeneity of the variance (Levene’s) for the two films from the data in the movie data file.

B. Write a few sentences describing the assumptions required in this exercise and whether or not they were met. Include information from the output to support your answers.

Describe the data, using summary statistics and graphs, as appropriate. Calculate the pair-wise correlation coefficients between Exports and each of the other variables. Test the statistical significance of each correlation coefficient.

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The relationship between firm exports, size, productivity and skill/capital intensity

Firm-level exports are potentially affected by a number of factors including the size of a firm, its productivity as well as the skill and capital intensity of its production technology.

The objective of this project is to establish whether size, productivity, skill intensity and capital intensity are determinants of firm exports in a cross-section of firms.

The data below contains information, covering a sample of 60 firms, on firm exports (Exports), a commonly used measure of firm size and in particular the number of employees of the firm (Empl), a measure of the productivity of the firm (Prod), as well as a measure of the skill intensity (Skill) and capital intensity (Capit) of the firm. Exports are measured in million pounds while productivity is measured as the ratio of the value of sales to the value of inputs used. Skill intensity is measured as the average number of years of schooling of the employees while capital intensity is measured as the ratio between the capital stock of a firm in million pounds and the number of employees.

1. Describe the data, using summary statistics and graphs, as appropriate. <check the example project for what the appropriate graph is>

1. Calculate the pair-wise correlation coefficients between Exports and each of the other variables. Test the statistical significance of each correlation coefficient. (Have to clearly spell out what is a null and alternative hypothesis, what is the test statistic you’re using, how it is distributed, what is the critical value and what is the value of statistic).

1. Consider the two variables Skill and Capit. Compute the pairwise correlation of the two variables and test the significance of the correlation coefficient.

1. Consider again the two variables Skill and Capit and test the null hypothesis that the two variables have equal variance. <look at the Lecture 4/ Lecture 5 material for this> (Again, have to clearly spell out what is a null and alternative hypothesis, what is the test statistic you’re using, how it is distributed, what is the critical value and what is the value of statistic).

1. Estimate a regression model of the form:

Exportsi =α + β1Empli + β2Prodi + β3Skilli + β4Capiti +ui

where the i subscript corresponds to firm i. Provide regression table and interpret the coefficients that you obtain, and comment on their economic and statistical significance. Statistical significance with a T test. To say whether it is big or small, use elasticities.

1. Interpret the R2 statistic from the regression and test whether it is statistically significant. (Again, the same steps, have to clearly spell out what is a null and alternative hypothesis, what is the test statistic you’re using, how it is distributed, what is the critical value and what is the value of statistic).

1. Re-estimate the model excluding the Capit variable and comment on any changes to the results and goodness of fit:

Exportsi =α + β1Empli + β2Prodi + β3Skilli +ui

1. Estimate a partial log-version of the regression model of the form:

Ln(Exports)i =α + β1Ln(Empl)i + β2Ln(Prod)i + β3Skilli + β4Capiti +ui

where the i subscript corresponds to firm i and Ln is the natural logarithm. Interpret the coefficients that you obtain, and comment on their economic and statistical significance. Compare this model with the one estimated in point 6.

1. What conclusions do you draw from your analysis?

Write, describe, summarize the nuclear disasters that occurred at Chernobyl and Fukushima & discuss what has been learned from those mistakes (human error).

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Chernobyl

Write, describe, summarize the nuclear disasters that occurred at Chernobyl and Fukushima & discuss what has been learned from those mistakes (human error).

What are your thoughts regarding this technology? Do you think this technology will continue to grow? Why or why not?

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Emerging Technologies

Highlight an emerging technology that relates to renewable energy.

What are your thoughts regarding this technology?

Do you think this technology will continue to grow? Why or why not?

Post additional photos or web links or current event article and summarize what the photo or video or article means to you.

In at least 250 word minimum

Analyze a spring mass system using hooke’s law and a best fit line. Determine if a rubber band obeys hooke’s law combine qualitative observations of a model

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Hooke’s lab

Analyze a spring mass system using hooke’s law and a best fit line. Determine if a rubber band obeys hooke’s law
combine qualitative observations of a model

Using computer drawing, you will use your design to explain how to actuate a first, second, and third class lever hydraulic system we discussed previously.

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HW2: Fluid Power DCV Design Challenge

To deepen your understanding of DCVs and their operation in a fluid power circuit, you will use computer drawing tools to design a basic two-position, 4-way, directional control valve and explain how it works. Using computer drawing, you will use your design to explain how to actuate a first, second, and third class lever hydraulic system as we discussed previously.