MATH 533 Statistics Course

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MATH 533 Statistics Course
For each of the five variables, process, organize, present and summarize the data. Analyze each…

Description

MATH 533 Statistics Course

MATH 533 Statistics Course

A+ Course Project Week 2, 6, 7| Discussions Week 1-7| Final Exam

If your assignments are different, please let us know.  We can help and provide a 100% correct solutions.

AJ Davis Department Course Project Week 2, 6, 7

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MATH 533 Statistics Course

AJ Davis Department Course Project Week 2 

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PROJECT PART A: Exploratory Data Analysis

  • Open the files for the Course Project and the data set in Doc Sharing.
  • For each of the five variables, process, organize, present and summarize the data. Analyze each variable by itself using graphical and numerical techniques of summarization. Use MINITAB as much as possible, explaining what the printout tells you. You may wish to use some of the following graphs: stem-leaf diagram, frequency/relative frequency table, histogram, boxplot, dotplot, pie chart, bar graph. Caution: not all of these are appropriate for each of these variables, nor are they all necessary. More is not necessarily better. In addition be sure to find the appropriate measures of central tendency, the measures of dispersion, and the shapes of the distributions (for the quantitative variables) for the above data. Where appropriate, use the five number summary (the Min, Q1, Median, Q3, Max). Once again, use MINITAB as appropriate, and explain what the results mean.
  • Analyze the connections or relationships between the variables. There are ten possible pairings of two variables. Use graphical as well as numerical summary measures. Explain what you see. Be sure to consider all 10 pairings. Some variables show clear relationships, while others do not.
  • Prepare your report in Microsoft Word, integrating your graphs and tables with text explanations and interpretations. Be sure that you have graphical and numerical back up for your explanations and interpretations. Be selective in what you include in the report. I’m not looking for a 20 page report on every variable and every possible relationship (that’s 15 things to do).
  • In particular, what I want you do is to highlight what you see for three individual variables (no more than 1 graph for each, one or two measures of central tendency and variability (as appropriate), the shapes of the distributions for quantitative variables, and two or three sentences of interpretation). For the 10 pairings, identify and report only on three of the pairings, again using graphical and numerical summary (as appropriate), with interpretations. Please note that at least one of your pairings must include the qualitative variable and at least one of your pairings must not include the qualitative variable.

Preview:

AJ Davis department has many credit customers in their store. They decided to select 50 customers that use credit collection to explore customer needs. The department used 5 variables to explore customer needs to aid in planning and growth. The variables included; location, income, credit balance, and size. The department…

MATH 533 Statistics Course

AJ Davis Department Course Project Week 6 

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Project Part B: Hypothesis Testing and Confidence Intervals

  1. Using the sample data, perform the hypothesis test for each of the above situations in order to see if there is evidence to support your manager’s belief in each case a.-d.  In each case use the Seven Elements of a Test of Hypothesis, in Section 6.2 of your text book, using the α provided by your Instructor in the Doc Sharing materials, and explain your conclusion in simple terms.  Also be sure to compute the p-value and interpret.
  2. Follow this up with computing confidence intervals (the required confidence level will be provided by your Instructor) for each of the variables described in a.-d., and again interpreting these intervals.
  3. Write a report to your manager about the results, distilling down the results in a way that would be understandable to someone who does not know statistics.  Clear explanations and interpretations are critical.

Preview:

We are 95% confident that the credit customer of AJ Davis department stores earns more than more than $45,000. We therefore reject managers’ speculations that average income of credit customers is < $45000 at 0.05 level of significance.  From the figure below…

MATH 533 Statistics Course

AJ Davis Department Course Project Week 7 

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Project Part C: Regression and Correlation Analysis

Your Instructor will specify for you the dependent variable and the independent variables in your Case and data.  Using MINITAB perform the regression and correlation analysis for the data by answering the following.

  1. Generate a scatterplot for the specified dependent variable and the specified independent variable, including the graph of the “best fit” line. Interpret.
  2. Determine the equation of the “best fit” line, which describes the relationship between the dependent variable and the selected independent variable.
  3. Determine the coefficient of correlation. Interpret.
  4. Determine the coefficient of determination. Interpret.
  5. Test the utility of this regression model (use a two tail test with the α provided by your Instructor). Interpret your results, including the p-value.
  6. Based on your findings in 1-5, what is your opinion about using the designated independent variable to predict the designated dependent variable? Explain.
  7. Compute the confidence interval for beta-1 (the population slope), using the confidence level specified by your Instructor.  Interpret this interval.
  8. Using an interval, estimate the average for the dependent variable for a selected value of the independent variable (to be provided by your Instructor). Interpret this interval.
  9. Using an interval, predict the particular value of the dependent variable for a selected value of the independent variable (to be provided by your Instructor). Interpret this interval.
  10. What can we say about the value of the dependent variable for values of the independent variable that are outside the range of the sample values? Explain your answer.

In an attempt to improve the model, we will attempt to do a multiple regression model predicting the dependent variable based on all of the independent variables.

11.  Using MINITAB run the multiple regression analysis using the designated dependent and independent variables.  State the equation for this multiple regression model.

12.  Perform the Global Test for Utility (F-Test). Explain your conclusion.

13.  Perform the t-test on each independent variable. Explain your conclusions and clearly state how you should proceed. In particular, which independent variables should we keep and which should be discarded. If any independent variables are to be discarded, re-run the multiple regression, including only the significant independent variables, and include the final Minitab output, with interpretation.

14.  Is this multiple regression model better than the linear model that we generated in parts 1-10? Explain.

Preview:

Interpretation: Income and time in years explains 79.21% of the variations in the credit balanced. Increase in income has a effect of increase credit balance while increase in time (years) seems to..

MATH 533 Statistics Entire Course

Discussions Week 1-7

All Students Posts 502 Pages 

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Descriptive Stats: Ethics and Workplace Applications Discussions Week 1 All Students Posts 93 Pages 

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Statistics in Action Case “Factors That Influence a Doctor to Refuse Ethics Consultation”

Before getting into analyzing the data, let’s consider the question of the pros and cons of doctors using ethics consultations with doctors, and other ethicists, trained to think and provide advice on ethical issues in healthcare. Take a look on the Internet, or in the Keller Graduate School online library, to find an article or articles on this issue. What is your view? Do you have any personal experiences you are comfortable sharing about medical ethical issues you and your family and/or friends have confronted?…

Case: Let’s Make a Deal Discussions Week 2 All Students Posts 85 Pages 

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A number of years ago, there was a popular television game show called Let’s Make a Deal. The host, Monty Hall, would randomly select contestants from the audience and, as the title suggests, he would make deals for prizes. Contestants would be given relatively modest prizes and then would be offered the opportunity to risk that prize to win better ones.

Suppose you are a contestant on this show. Monty has just given you a free trip worth $500 to a locale that is of little interest to you. He now offers you a trade: Give up the trip in exchange for a gamble. On the stage are three curtains, A, B, and C. Behind one of them is a brand-new car worth $45,000. Behind the other two curtains, the stage is empty.

You decide to gamble and give up the trip. (The trip is no longer an option for you.) You must now select one of the curtains. Suppose you select Curtain A.

In an attempt to make things more interesting, Monty then exposes an empty stage by opening Curtain C (he knows that there is nothing behind Curtain C). He then asks you if you want to keep Curtain A, or switch to Curtain B.  What would you do?…

Workplace Applications, Normal Distribution and Sampling Distributions Discussions Week 3 All Students Posts 62 Pages 

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What is a “normal” population?  Our work this week introduces Normally distributed population to us, as well as Sampling distributions and the Central Limit Theorem.

Please review my posts below and respond.  In your responses, try to avoid just “giving the answer”.  If the question requires a calculation, explain what you did or show the major steps involved in the calculation.  We rarely want a “short, simple” answer!  It is always best to give the answer, and then explain how you arrived at the result.

You’ll notice that I post several questions.  You are not required to answer/work each question; I simply post questions to provide plenty of opportunity for responding to “new” material in the discussion.  Respond to as many of my posts as you wish.

Remember to SHOW YOUR WORK so everyone can see your solution method.  If you use Minitab, be sure to describe or list the specific commands used….

Case: Statistics in Action: Medicare Fraud Investigations Discussions Week 4 All Students Posts 75 Pages 

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Read the selection in your textbook pertaining to the Case: Statistics in Action: Medicare Fraud Investigations; load the data set for the case, MCFRAUD, into Minitab; answer the question about the case in the Discussion area; and likewise read and respond to the follow-on selections in the textbook for the case in the Statistics in Action Revisited.  What is a point estimate of the mean overpayment?…

Case: Statistics in Action: Diary of a Kleenex User Discussions Week 5 All Students Posts 70 Pages 

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Read the selection in your text book pertaining to the Case: Statistics in Action: Diary of a Kleenex® User; load the data set for the case, TISSUES, into Minitab; answer the question about the case in the Discussion area; and likewise read and respond to the follow-on selections in the textbook for the case in the Statistics in Action Revisited. How would you briefly summarize the case, and the data that was generated?…

Case: Statistics in Action: Legal Advertising-Does It Pay?  Discussions Week 6 All Students Posts 62 Pages

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Read the Case: Statistics In Action: Legal Advertising—Does It Pay?, and answer the following questions. (The case is included in your textbook, Chapter 10.) The data set for the case study is LEGALADV, and it is available in your textbook resources, so you don’t have to enter the data!  Summarize what the case is about, and what the variables represent….

Case: Statistics in Action: Bid-Rigging in the Highway Construction Industry Discussions Week 7 All Students Posts 55 Pages 

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Read the Case: Statistics in Action: Bid-Rigging in the Highway Construction Industry, in Chapter 11 of your textbook, and answer the following questions. The data set, FLAG, for the case study is available in the publisher’s website, so you don’t need to enter the data into Minitab by hand. What is this case about? Describe the key variables…

MATH 533 Statistics Entire Course

Final Exam 

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(TCO A) A random sample of 20 cars driving down I-294 is selected and their speed is monitored.  The results are as follows (in mph).

68        65        50        79        77        60        55

61        78        75       

75        67        72        58        70        62        67

72        70        74

  1. Compute the mean, median, mode, and standard deviation, Q1, Q3, Min, and Max for the above sample data on speed per car.
  2. In the context of this situation, interpret the Median, Q1, and Q3. (Points: 33)

(TCO B) Consider the following data on newly hired employees in relation to which part of the country they were born and their highest degree attained.

  HSBSMSPHDTotal
East 352111
Midwest 792018
South 586221
West 178622
 Total162918972

Of you choose one person at random, then find the probability that the person

  1. Has a PHD
  2. is from the East and has a BS as the highest degree arraigned
  3. has only a HS degree, given that person is from the West. (Points: 18)

(TCO B) Midwest Airlines has had an 80% on time departure rate.  A random sample of 20 flights is selected.  Find the probability that

  1. exactly 15 flights depart on time in the sample
  2. at least 17 flights depart on time in the sample
  3. less than 11 flights depart on time in the sample. (Points: 18)

(TCO B) The Federal Government is stepping up efforts to reduce average response times of fire departments to fire calls.  The distribution of mean response times to fire calls follows a normal distribution with a mean of 12.8 minutes and a standard deviation of 3.7 minutes.

  1. Find the probability that a randomly selected response time is less than 15 minutes.
  2. Find the probability that a randomly selected response time is less than 13 minutes.
  3. The fastest 20% of fire departments will be singled out for a special safety award. How fast must a fire department be I order to qualify for the special safety award?  (Points: 18)

(TCO C) A transportation company wants to estimate the average length of time goods are in transit across country.  A random sample of 20 shipments yields the following results.

Sample Size = 20

Sample Mean = 4.6 days

Sample Standard Deviation = 1.50 days

  1. Compute the 90% confidence interval for the population mean transit time.
  2. Interpret this interval.
  3. How many shipments should be sampled if we wish to generate a 99% confidence interval for the population mean transit time that is accurate to within .25 days? (Points: 18)

(TCO C) United Express Delivery is interested in estimating the percentage of packages delivered damaged.  A simple random sample of 500 packages yields 12 delivered damages and 488 delivered undamaged.

  1. Compute the 99% confidence interval for the population proportion of packages that are delivered damaged.
  2. Interpret this confidence interval
  3. How many packages should be sampled in to order to be 99% confident of being within .5% of the actual population proportion of packages delivered damaged? (Points: 18)

(TCO D) A manager at Travis Savings and loan believes that less than 52% of their depositors won their homes.  A random sample of 100 depositors is selected with the results that 46 depositors own their homes and the other 54 do not own their homes.  Does the sample data provide evidence to conclude that less than 52% of all depositors at Travis Savings and Loan own their homes (with α = .05)?  Use the hypothesis testing procedure outlined below.

  1. Formulate the null and alternative hypotheses.
  2. State the level of significance.
  3. Find the critical value (or values), and clearly show the rejection and nonrejection regions.
  4. Compute the test statistic.
  5. Decide whether you can reject Ho and accept Ha or not.
  6. Explain and interpret your conclusion in part e. What does this mean? 
  7. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
  8. Does the sample data provide evidence to conclude that less than 52% of all depositors at Travis Savings and Loan own their homes (with α = .05)? )Points: 24)

(TCO D) Bill Smith is the Worthington Township manager.  When citizens request a traffic light, the staff assesses the traffic flow at the requested intersection.  Township policy requires the installation of a traffic light when an intersection averages more than 150 vehicles per hour.  A random sample of 48 vehicles counts is done.  The results are as follows:

Sample Size = 48

Sample Mean = 158.3 vehicles/hr.

Sample Standard Deviation = 27.6 vehicles/hr.

Does the sample data provide evidence to conclude that the installation of the traffic light is warranted (using α = .10)?  Use the hypothesis testing procedure outlined below.

  1. Formulate the null and alternative hypotheses
  2. State the level of significance.
  3. Find the critical value (or values), and clearly show the rejection and norejection regions.
  4. Compute the test statistic
  5. Decide whether you can reject Ho and accept Ha or not.
  6. Explain and interpret your conclusion in part e. What does this mean? 
  7. Find the observed p-value for the hypothesis test and interpret this value. What does this mean?
  8. Does this sample data provide evidence (with α = 0.10), that the installation of the traffic light is warranted? (Points; 24)

(TCO E) The management of JAL Airlines assumes a direct relationship between advertising expenditures and the number of passengers who choose to fly JAL.  The following data is collected over the past 15 months of performance by JAL Airlines.  Note that X=ADEXP (Advertising Expenditures in $1,000s), and Y=Passengers (number of passengers in 1,000s).  The MINITAV printout can be found below.

ADEXP PASSANGERS PREDICT
100 15 120
120 17 250
80 13  
170 23  
100 16  
150 21  
100 14  
140 20  
190 24  
100 17  
110 16  
130 18  
160 23  
100 15  
120 16  

MATH 533 Statistics Course

  1. Analyze the above output to determine the regression equation.
  2. Find and interpret in the context of this problem.
  3. Find and interpret the coefficient of determination (r-squared).
  4. Find and interpret coefficient of correlation.
  5. Does the data provide significant evidence (α = .05) that advertising expenditures can be used to predict the number of passengers? Test the utility of this model using a two-tailed test.  Find the observed p-value and interpret.
  6. Find the 95% confidence interval for the mean number of passengers when advertising expenditures were $120,000. Interpret this interval.
  7. Find the 95% prediction interval for the number of passengers when advertising expenditures were $120,000. Interpret this interval.
  8. What can we say about the number of passengers when advertising expenditures were $250,000? (Points : 48)

Prediction for PASSANGERS

(TCO E) A newly developed low-pressure snow tire has been tested to see how it wears under normal dry weather conditions.  Twenty of these tires were tested on standard passenger cars.  These cars were driven at high speeds on a dry test track for varying lengths of time.  We are interested in finding the relationship between hours driven (HOURS, X1), brand of car driven (BRAND, X2, where 0=Ford and 1 =General Motors), and tread wear (TREAD, Y in inches).  The data is found below.

HoursBrandTread
1300.1
2500.2
2700.2
4600.3
1800.1
3100.2
4600.3
5700.4
7500.5
8700.6
6210.4
10510.7
8810.6
6310.4
7710.5
10910.7
11710.8
3510.2
9810.6
12110.8

 

  1. Analyze the above output to determine the multiple regression equation
  2. Find and interpret the multiple index of determination (R-Sq).
  3. Perform the multiple regression t-tests on (use two tailed test with (α = .10). Interpret your results.
  4. Predict the tread wear for tires from General Motors that were driven for 50 hours. Use both a point estimate and the appropriate interval estimate. (Points: 31)

MATH 533 Statistics Course

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