# Inferential Research and Statistics Project

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* **University of Phoenix Material*

Inferential Research and Statistics Project

Part 1

**Select** one of the following scenarios based on your particular field of interest in psychology:

**General Psychology:**- Clinicians at a small clinic have been introduced to a new method to treat post-traumatic stress disorder (PTSD) in their clients for veterans. Research indicates that virtual reality (VR) is a highly effective treatment option for patients with PTSD. Currently, the clinic uses only cognitive processing therapy (CPT) with their patients suffering from PTSD. The clinicians would like to find out whether VR therapy has different results from CPT therapy. The measure used by the clinic to measure PTSD symptoms is the Combat Exposure Scale. Both therapies need to be applied for a minimum of 12 weeks to be effective.

**Write** a 525- to 750-word paper that addresses the following for your chosen scenario:

- Clearly define the problem or issue you are addressing. Provide a brief background of any research you have found that might affect your research hypothesis.
- Create a research hypothesis based on the information provided in each scenario. You have been given a data set (Excel document) with two sets of interval data (just the numbers, as you must decide what they represent, such as method A results or method B results). This means you are going to test one thing against another, such as which method works best (step 1 of the steps to hypothesis testing). State the null and research hypotheses. Explain whether these hypotheses require a one-tailed test or two-tailed test, and explain your rationale.
- Describe the sample you will use. Sample size will be 30 for each group, which are provided in your data set. Explain what type of sampling you selected.
- Do you think you would also collect some descriptive data, such as gender, age, or shift? Why do you think it makes sense to collect descriptive data?

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**Format** your paper according to APA guidelines.

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*Example*

You have a hypothesis that two drugs have different effects on lowering anxiety. You would have anxiety scores for drug A and anxiety scores for drug B (all after 4 weeks of treatment) to run inferential analysis for after 4 weeks.

- Null hypothesis is H
_{0}: drug A = drug B - Research hypothesis is H
_{1}:_{ d}rug A ≠ drug B - Dependent variable: Anxiety score changed after treatment.
- Independent variable: drug treatment

Because you did not state a direction in your hypotheses (better than or worse than), this will be a two-tailed test. You are looking for differences in either direction. You would set your alpha level of .05 and have a sample for each group of 30 people that were volunteers for the study.

- Provide the main finding of the study. What did you prove or fail to prove?
- Provide recommendations based on your findings.

**Format** any citations in your presentation according to APA guidelines.

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# Assignment help-Unit: TSTA101 – INTRODUCTORY STATISTICS

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Individual Assignment

Unit: TSTA101 – INTRODUCTORY STATISTICS

Due Date: Thursday, 28/09/2017 (16:00pm)

Number of Questions: Six (6) Questions

Total Marks: Twenty (20) marks

Instructions: All questions should be attempted.

The marks of each question would be awarded based on your understanding of the questions, concepts and procedures; hence you should demonstrate your answers step by step.

Question 1 [3 marks]

Part a)

Find the following probabilities by checking the z table

i) P((Z>-0.8)

ii) P (-1.3<Z<-0.7)

iii) Z0.2

Part b)

A new car has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 4 miles. Find the probability of the following events.

i) The car travels more than 70 miles per gallon.

ii) The car travels less than 60 miles per gallon.

iii) The car travels between 55 and 70 miles per gallon.

Question 2 [3 marks]

Part a)

A sample of n=25 observations is drawn from a normal population with μ=100 and σ=20. Find the following.

i) P(<96)

ii) P(96<<105)

Part b)

The amount of time the university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours.

i) What is the probability that a professor works for more than 60 hours per weeks?

ii) Find the probability that the mean amount of work per week for three randomly selected professors is more than 60 hours?

Question 3 [2 marks]

Part a)

Given the following information =500, σ=12, n=50

i) Determine the 95% confidence interval estimate of population mean.

ii) Determine the 99% confidence interval estimate of population mean.

Part b)

A statistics practitioner calculated the mean and standard deviation from a sample of 51. They are =120 and s=15.

(i) Estimate the population mean with 95% confidence level.

(ii) Estimate the population mean with 99% confidence level.

X

X

X

X

Question 4 [4 marks]

Part a)

Calculate the statistic, set up the rejection region, interpret the result, and draw the sampling distribution.

H0: μ=10

H1: μ≠10

Given that: σ=10, n=100, =10, α=0.05.

Part b)

A statistics practitioner is in the process of testing to determine whether is enough evidence to infer that the population mean is different from 180. She calculated the mean and standard deviation of a sample of 200 observations as =175 and s=22. Calculate the value of the test statistic of the test required to determine whether there is enough evidence to infer at the 5% significance level that the population mean is different from 180.

Question 5 (2 marks)

Suppose you are using a completely randomized design to study some phenomenon.

There are five treatment levels and a total of 55 people in the study. Each treatment

level has the same sample size. Complete the following ANOVA. Use α=0.05 to find the table F value and use the data to test the null hypothesis.

Source of Variance

SS

df

MS

F

Treatment

583.39

Error

972.18

Total

1555.57

Question 6 (6marks)

There is a simple linear regression model given by:

where price = used car price in dollars and

age = age of the car in years.

The EXCEL results obtained using Ordinary Least Squares are presented below:

Regression Statistics

R2

0.077

Standard Error

42069

Observations

117

Coefficients

Standard Error

t Stat

Intercept

A

6748

7.035

Age

-2658

856

B

Use the above output for answering the following questions:

a) Calculate the missing values from the summary output: A and B

b) Interpret the slope of the regression line.

c) Write down the estimated linear regression line.

d) What is the value of the coefficient of determination? Interpret this value

e) What is the value of the coefficient of correlation? Interpret this value.

f) Test whether the estimated coefficient of Age is significantly less than zero at the 5% level of significance.

g) Predict price if the car has driven 3 years. X

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# CEE 213—Deformable Solids The Mechanics Project: http://customwritings-us.com/orders.php

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CEE 213—Deformable Solids The Mechanics Project

Arizona State University CP 3—Properties of Areas

1

Computing Project 3

Properties of Areas

The computing project Properties of Areas concerns the computation of various properties

of cross sectional areas. In each of our theories (i.e., axial bar, torsion, and beams) we arrive

at a point where we need certain properties of the cross section to advance the analysis. For

the axial bar we needed only the area; for torsion we needed the polar moment of inertia;

for the beam we will need moment of inertia of the cross section about the centroid of the

cross section.

We can develop an algorithm that allows the computation of all of the properties of a cross

section if the cross section can be described as a polygon. The algorithm is built on formulas

for the properties of a triangle. What that program will do is create a triangle from the

origin and the two vertex nodes associated with a side of the polygon. Whether this polygon

adds or subtracts from the accumulating properties will be determined from the vectors

defining the sides of the polygon (see the CP Notes for further clarification). If you loop

over all of the sides, the end result will be the properties of the entire cross section.

The general steps are as follows:

1. Develop a routine that allows you to describe the cross section with a sequence of

points numbered in a counterclockwise fashion starting with 1. The last point

should be a repeat of the first one in order to close the polygon. Some suggestions:

a. Store the (x,y) coordinates of each point in a single array x(N,2), where N

is the number of points required to describe the cross section (including

the repeat of the first point as the last point) and the first column contains

the x values of the coordinate and the second column contains the values

of the coordinate and the second column contains the y value.

b. It will eventually be a good idea to put the input into a MATLAB function

and call the function from your main program. That way you can build up

a library of cross sectional shapes without changing your main program.

c. If you need a negative area region (for a cutout section like in an open

tube) then number the points in that region in a counter-clockwise fashion.

Just keep numbering the vertices in order (no need to start over for the

negative areas).

2. Develop a routine to loop over all of the edges of the polygon and compute (and

accumulate) the contributions of the triangle defined by the vectors from the origin

to the two vertices of the current side of the triangle (that gives two sides) and the

CEE 213—Deformable Solids The Mechanics Project

Arizona State University CP 3—Properties of Areas

2

vector that points from the first to the second vertex (in numerical order). Calculate

the area, centroid, and outer-product contributions to the properties (see the CP

Notes for clarification of this issue).

3. Compute the orientation of the principal axes of the cross section using the eigenvalue

solver in MATLAB (eig) on the moment of inertia matrix J. See the CP

Notes for more information on this task.

4. Create an output table (print into the Command Window) giving the relevant cross

sectional properties. Develop a routine to plot the cross section. Include the location

of the centroid of the cross section in the graphic (along with lines defining

the principal axes if you can figure out how to do that).

5. Generate a library of cross sections, including some simple ones (e.g., a rectangular

cross sections) to verify the code. Include in your library as many of the following

cross sections as you can get done:

a. Solid rectangle with width b and height h.

b. Solid circle of radius R.

c. Rectangular tube with different wall thickness on top and bottom.

d. I-beam with flange width b, web depth d, flange thickness tf, and web

thickness tw.

e. Angle section with different leg lengths and leg thicknesses.

f. Circular tube with outside radius R and wall thickness t.

g. T-beam.

6. Use the program to explore aspects of the problem. For example,

a. Why is it more efficient to use an open circular tube for torsion rather than

a solid cylinder?

b. For beam bending we can control deflections and reduce stresses with a

large moment of inertia about the axis of bending. Show the trade-offs

available in an I-beam when you can select different web and flange depths

and thicknesses. What is the ideal allocation of material? Why would we

never actually do that in practice?

c. Demonstrate that the principal axes of a symmetric cross section lie along

the lines of symmetry. You can do this by showing that the off-diagonal

elements of J are zero for symmetric sections with axes so chosen.

d. Explore any other feature of the problem that you find interesting.

CEE 213—Deformable Solids The Mechanics Project

Arizona State University CP 3—Properties of Areas

3

Write a report documenting your work and the results (in accord with the specification

given in the document Guidelines for Doing Computing Projects). Post it to the Critviz

website prior to the deadline. Note that there is only one submission for this problem (the

final submission).

Please consult the document Evaluation of Computing Projects to see how your project

will be evaluated to make sure that you can get full marks. Note that there is no peer review process for reports in this course.

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