Tag: statistics

Statistics

Posted on | by
The following problems must be completed by hand except where noted.  You are highly encouraged to verify your results in Excel.  However, an Excel spreadsheet will not be submitted and all work must be shown on paper.  Final submission is in the form of a pdf document.
Problem 1
A technician at a steel mill records the results of a tension coupon test on three different random steel plates per day over a period of 5 days.  The yield strength in megapascals is a measure of the largest stress the material can support before permanent deformation occurs.
Day Yield Strength (MPa)
1 350 367 345
2 339 329 360
3 343 353 359
4 325 380 346
5 351 359 341
Assume that each measurement is xi and the total number of measurements in the sample is n.  You may not use Excel to complete your calculations.
a) Calculate the Yield Strength sum as ∑𝑥!.
b) Determine the mean Yield Strength.
c) Calculate the sum ∑𝑥!” for the sample.
d) Determine the standard deviation of the sample.
e) Group the data into approximately equal bins and construct a frequency distribution table.  The Yield Strength bins should be <335, 336-345, 346-355, 356-365, 366-375 and >375.
f) Draw a histogram of the distribution.  You may present this chart using Excel output.
Problem 2
Strain gauges were mounted on a structure and recorded the strain (e) versus stress (s) as load was applied to the structure.  Two different locations were recorded.
  Location 1 Location 2
Strain 𝜖 Stress 𝜎 (Mpa) Stress 𝜎 (Mpa)
0 90 208
0.0001 132 229
0.0002 154 244
0.0003 180 224
0.0004 206 247
0.0005 221 282
0.0006 231 330
0.0007 273 312
0.0008 250 311
0.0009 305 364
We are interested in obtaining the linear relationship between the strain (e) and stress (s).  For Location 1, analysis showed the material stress s followed the relationship
𝜎=214000𝜖+108
This relationship shows there is a residual stress 𝜎#$ of 108 MPa already existing on the structure, when the applied strain e is zero.  The material modulus of elasticity, E, is 214 000 MPa.
You are expected to develop a similar relationship for Location 2.  You should consider strain as the independent variable X, and stress as the dependent variable Y.
a) Calculate ∑𝑋!.
b) Calculate ∑𝑌!.
c) Calculate ∑𝑋!𝑋!.
d) Calculate ∑𝑌!𝑌!.
e) Calculate ∑𝑋!𝑌!.
f) Using the least squares approach, calculate the slope m and y-intercept b for the straight line which best fits the data for Location 2.  You may NOT use Excel.
g) Calculate the coefficient of correlation, r, for the line found in step f.  You may NOT use Excel.

Statistics

Posted on | by
The following problems must be completed by hand except where noted.  You are highly encouraged to verify your results in Excel.  However, an Excel spreadsheet will not be submitted and all work must be shown on paper.  Final submission is in the form of a pdf document.
Problem 1
A technician at a steel mill records the results of a tension coupon test on three different random steel plates per day over a period of 5 days.  The yield strength in megapascals is a measure of the largest stress the material can support before permanent deformation occurs.
Day Yield Strength (MPa)
1 350 367 345
2 339 329 360
3 343 353 359
4 325 380 346
5 351 359 341
Assume that each measurement is xi and the total number of measurements in the sample is n.  You may not use Excel to complete your calculations.
a) Calculate the Yield Strength sum as ∑𝑥!.
b) Determine the mean Yield Strength.
c) Calculate the sum ∑𝑥!” for the sample.
d) Determine the standard deviation of the sample.
e) Group the data into approximately equal bins and construct a frequency distribution table.  The Yield Strength bins should be <335, 336-345, 346-355, 356-365, 366-375 and >375.
f) Draw a histogram of the distribution.  You may present this chart using Excel output.
Problem 2
Strain gauges were mounted on a structure and recorded the strain (e) versus stress (s) as load was applied to the structure.  Two different locations were recorded.
  Location 1 Location 2
Strain 𝜖 Stress 𝜎 (Mpa) Stress 𝜎 (Mpa)
0 90 208
0.0001 132 229
0.0002 154 244
0.0003 180 224
0.0004 206 247
0.0005 221 282
0.0006 231 330
0.0007 273 312
0.0008 250 311
0.0009 305 364
We are interested in obtaining the linear relationship between the strain (e) and stress (s).  For Location 1, analysis showed the material stress s followed the relationship
𝜎=214000𝜖+108
This relationship shows there is a residual stress 𝜎#$ of 108 MPa already existing on the structure, when the applied strain e is zero.  The material modulus of elasticity, E, is 214 000 MPa.
You are expected to develop a similar relationship for Location 2.  You should consider strain as the independent variable X, and stress as the dependent variable Y.
a) Calculate ∑𝑋!.
b) Calculate ∑𝑌!.
c) Calculate ∑𝑋!𝑋!.
d) Calculate ∑𝑌!𝑌!.
e) Calculate ∑𝑋!𝑌!.
f) Using the least squares approach, calculate the slope m and y-intercept b for the straight line which best fits the data for Location 2.  You may NOT use Excel.
g) Calculate the coefficient of correlation, r, for the line found in step f.  You may NOT use Excel.

Statistics

Posted on | by

 

 

 

 

 

Suppose you are a real estate agent and you were asked by a client about the “typical” home in a subdivision. Being the astute agent you are, you have gathered the following information on each house in the subdivision: Price, square footage, numbers of bedrooms, number of bathrooms, and age. What statistic (mean, median, or mode) would you use to describe each aspect of the typical home and why?

 

Statistics

Posted on | by Brian Leakey

Recall that samples are used to generate a statistic, which businesses use to estimate the population parameter. You have learned how to take samples from populations and use them to produce statistics. For two quantitative variables, businesses can use scatterplots and the correlation coefficient to explore a potential linear relationship. Furthermore, they can quantify the relationship in a regression equation.

You have submitted your initial analysis to the sales team at D.M. Pan Real Estate Company. You will continue your analysis of the provided Real Estate Data Spreadsheet spreadsheet (attached below) using your selected region to complete your analysis. You may refer back to the initial report you developed in the Module Two Assignment Template to continue the work. This document and the National Summary Statistics and Graphs Real Estate Data PDF spreadsheet will support your work on the assignment.

Regression Equation: Provide the regression equation for the line of best fit using the scatterplot from the Module Two assignment.
Determine r: Determine r and what it means. (What is the relationship between the variables?)
Determine the strength of the correlation (weak, moderate, or strong).
Discuss how you determine the direction of the association between the two variables.
Is there a positive or negative association?
What do you see as the direction of the correlation?
Examine the Slope and Intercepts: Examine the slopeb1 and intercept b0
Draw conclusions from the slope and intercept in the context of this problem.
Does the intercept make sense based on your observation of the line of best fit?
Determine the value of the land only.
Note: You can assume, when the square footage of the house is zero, that the price is the value of just the land. This happens when x=0, which is the y-intercept. Does this value make sense in context?
Determine the R-squared Coefficient: Determine the R-squared value.
Discuss what R-squared means in the context of this analysis.

Statistics

Posted on | by

Given the statistic that 6 out of 9 recent mass shootings were committed by men in the ’emerging adulthood” stage, what are some developmental and/or gender reasons this may be happening?

Developing a set of data, statistics, and data into an attention-grabbing

Posted on | by

 

 

 

 

Developing the ability to transform a set of data, statistics, and data into an attention-grabbing and engaging visual aid that emphasizes key points can be a challenging, but worthwhile, exercise. There are a number of useful resources to help identify appropriate visual aids by the type of data and how to use color to focus attention on key statistics. One type of visual aid is a Microsoft PowerPoint presentation.
For Part II of this Assessment, explore how PowerPoint can be used to create an effective presentation. Consider other types of visual aids that can be used to communicate criminal justice data. If you have not already, review the websites located in the Learning Activities to help find your data needed for this Assessment to locate the three data sources to support your argument. You are to create a 5- to 6-slide PowerPoint presentation. Your presentation should include:
• Title page.
• Per slide create YOUR OWN visual aid for each of the sets of data (for a total of three visual aids). These can include graphs, tables, pictures, etc. Your visual aids must be developed on your own and are not taken from another source (i.e., you will be creating your own charts and tables, are not copying an already created table or chart and turning it in, and must include the complete citation/reference for your submission and data).
• Reference page.3

Statistics

Posted on | by

 

1) For each of the data sets below, indicate which type of graph you would choose to display the data and why you would choose that graph:

a. Scores on an anxiety scale that range from “not anxious”, “somewhat anxious”, “moderately anxious” and “severely anxious”.

b. Number of psychology majors versus other majors in your statistics course

c. Mean speed (in seconds) to complete a set of puzzles – participants worked on either math puzzles or spatial navigation puzzles.

2) For each data set in the question above, list the variables present in the description and indicate if each variable is categorical or continuous.

 

Statistics

Posted on | by

 

Mary is planning a study to see if learning of 6th graders on a math lesson is affected by background noise level. She wants to use a t-test for independent groups to analyze her results. Help her plan her study. What is her independent variable (IV) here? Describe two conditions she could create for the IV in her study. What is her dependent variable (DV) here? Describe a way to measure the DV so that each participant would have one score at the end. Would this DV measure be on a continuous scale of measurement? Why is this important? Explain and justify.

Q1.b
Consider Mary’s experiment regarding whether learning of 6th graders on a math lesson is affected by background noise level. Mary has collected her data. What is the null hypothesis for her study? What is the alternative hypothesis for her study? What are the assumptions that must be met about her data before she can correctly use an independent t-test to test the hypotheses? Why? How would she see if her data met these assumptions? How much room does she have to violate any of these assumptions and still get accurate results from the t-test? Explain and support your answers.

Statistics

Posted on | by

 

 

In public health, data are often gathered from separate groups in order to describe health-related behavior for a topic of interest. In practice, a larger sample is often surveyed, and then focus groups or interviews can be conducted with a smaller subset of the sample. The quantitative survey data from a larger group helps to identify health-related trends and patterns within the sample group. The qualitative data collected with the smaller group complements the quantitative survey data and helps to determine why and how a phenomenon exists. The cumulative findings can then help public health professionals form a conclusion about the health issue and inform future public health research, policy, and practice.

The purpose of this assignment is to analyze qualitative and quantitative data from two separate groups, propose a research question, and then disseminate your findings in a mixed-methods manuscript. The survey and focus group are both on the topic of nutrition. The quantitative data is adapted from the Youth Risk Behavior Surveillance System (YRBSS), and the qualitative data is from a focus group transcript in which 9th grade girls discussed healthy eating.

For this assignment, you will use:

IBM SPSS Statistics and the “Youth Risk Behavior Surveillance System Dataset” to conduct a basic quantitative statistical analysis.
The “9th Grade Girls Healthy Food Focus Group Transcription” to conduct a qualitative analysis and identify key themes.

Using the resources indicated above, conduct the following analyses and record the results on the “Results and Outputs” template. Attach this document as an Appendix in your paper.

Qualitative Analysis: Read the “9th Grade Girls Healthy Food Focus Group Transcription.” This transcript is from a focus group of 9th grade girls discussing healthy eating with the moderator. Generate codes and summarize the qualitative data.

Quantitative Analysis:

Review the “Youth Risk Behavior Surveillance System Dataset.” Identify two or three variables of interest and identify a study topic for your paper. Conduct a literature search for three to five peer-reviewed articles from the last 5 years that have studies supporting your topic. Develop a research question for your study based on the selected variables. The research question should demonstrate support for the focus group results and should be supported by existing literature.
Prepare the data to complete the analysis based on your research question.
Using SPSS, conduct descriptive statistics to summarize the sample.
Using SPSS, select an appropriate quantitative inferential statistical test to analyze the data.
Part 2: Reporting Data

Prepare a 1,250-1,500 word manuscript to disseminate the findings of your proposed study. The study should be based on your proposed research question and supported by the findings from the qualitative and quantitative analyses above, as well as by current literature. Include the following:

Abstract

A 150-250 word summary of the manuscript.
Introduction

Summarize the purpose of the research, the problem being addressed, and your proposed research question.
Support your summary using three to five peer-reviewed articles from the last 5 years that are relevant to your topic and that support why the study is being conducted.
Methods

Qualitative Methods (Focus Group)

Describe the focus group sample and data collection process.
Describe the process used to analyze the qualitative data.
Quantitative Methods (YRBSS Survey)

Discuss how the data were collected.
Identify and describe the variables used in the analysis.
Describe the descriptive and inferential statistical tests that were conducted.
Identify the software that was used to conduct the analysis.

 

Statistics

Posted on | by

 

Let XI, , X.„ be a random sample taken from a Norma/(ps. a2) distribu-tion with some known a. The testing is done between Ho : p = po and HI : p = pi where pi > po. The rejection region of the test is defined as (X > k) for sonic constant k. Suppose that the significance level a is specified. Prove that the power of this test can be written as power = 1 — 4F (4r-`(1 a) aR/Ti Po) where $ denotes the cdf of the standard normal distribution.