## Differentiate between the appropriate and inappropriate application and interpretation of research methods and statistics.

Write a brief research report (up to about 7 pages, not including title page, abstract, and references), based on an analysis of the data file. Choose a hypothesis, cite at least three references to justify your hypothesis, test your hypothesis with an analysis of the DATA540.SAV file, and then report and discuss the results. Your results should include both descriptive and inferential statistics.  Please make sure your report is submitted by the due date to ensure ample time for mentor feedback, and possible integration of feedback and revision if necessary.

Compare/contrast the basic assumptions underlying various statistical operations
Summarize the consequences of using various methodological approaches
Differentiate between the appropriate and inappropriate application and interpretation of research methods and statistics

## What information does the strength of a correlation coefficient convey?

What information does the strength of a correlation coefficient convey?

#2.  State whether each of the following is an example of a positive correlation or a negative correlation.

Higher education level is associated with a larger annual income.
Increased testosterone is associated with increased aggression.
The smaller the class size, the more students believe they are receiving a quality education.
Rising prices of apples are associated with the sale of fewer apples.

#3.  Which is the predictor variable (X) and which is the criterion variable (Y) for each of the following examples?

A researcher tests whether the size of an audience can predict the number of mistakes a student makes during a classroom presentation.
A military officer tests whether the duration of an overseas tour can predict the morale among troops overseas.
A social psychologist tests whether the size of a toy in cereal boxes can predict preferences for that cereal.

## Explain the difference between the objective function and the constraints.

Select one (1) of the following topics for your primary discussion posting:

The objective function always includes all of the decision variables, but that is not necessarily true of the constraints. Explain the difference between the objective function and the constraints. Then, explain why a constraint need not refer to all the variables.
Pick any constraint from any problem in the text, and explain how to plot the line that corresponds to that constraint.

## What is a confidence interval?

Week 5 Discussion
Constructing Confidence Intervals

What is a confidence interval?  What information do confidence intervals give you?
What advantages do confidence intervals give over a single number?
How do you compute a confidence interval?
Why do confidence intervals have two numbers?  What does each represent?
In the discussion for week 4, you rolled a pair of dice 10 times and calculated the average sum of your rolls.  Then you did the same thing with 20 rolls.  Use your results from the week 4 discussion for the average of 10 rolls and for the average of 20 rolls to construct a confidence interval for the true mean of the sum of a pair of dice (assume σ = 2.41, and you are doing a 95% confidence interval).
week 4’s roll + results

Roll

Sum

1

5,3

2

2,4

3

1,5

4

6,2

5

1,1

6

3,4

7

2,4

8

1,3

9

5,6

10

2,5
5+3=8
2+4=6
1+5=6
6+2=8
1+1=2
3+4=7
2+4=6
1+3=4
5+6=11
2+5=7
Sum of Total 65
Average = 65/10 = 6.5

Roll

Sum

1

2,5

2

3,1

3

5,5

4

2,3

5

6,3

6

1,5

7

5,4

8

6,4

9

3,1

10

2,2

11

4,1

12

5,4

13

6,3

14

3,2

15

5,3

16

1,1

17

4,3

18

2,1

19

6,1

20

4,4
2+5=7
3+1=4
5+5=10
2+3=5
6+3=9
1+5=6
5+4=9
6+4=10
3+1=4
2+2=4
4+1=5
5+4=9
6+3=9
3+2=5
5+3=8
1+1=2
4+3=7
2+1=3
6=1=7
4+4=8
Sum of Total = 131
Average = 131/20 = 6.55

What do you notice about the length of the interval for the mean of 10 rolls versus the mean of 20 rolls?  Did you expect this?  Why or why not?
What would happen to the length of the interval if the confidence level was 99% instead of 95%?  Why?  What if it were a 90% confidence interval?

Week 5 Assignment

Question 1
In a poll of 500 voters in a campaign to eliminate non-returnable beverage containers, 275 of the voters were opposed. Develop a 95% confidence interval estimate for the proportion of all the voters who opposed the container control bill.

Question 2
A random sample of 87 airline pilots had an average yearly income of \$97,000 with a standard deviation of \$3,000.

If we want to determine a 95% confidence interval for the average yearly income, what is the value of t?
What are the degrees of freedom for this problem, and how is this value calculated?
Develop a 95% confidence interval for the average yearly income of all pilots.

Question 3
In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 100 pieces of carry-on luggage was collected and weighed. The average weight was 34 pounds. Assume that we know the standard deviation of the population to be 5 pounds.

Determine a 90% confidence interval estimate for the mean weight of the carry-on luggage.
What determined whether you used a t value or a z value?

Question 4
A statistician employed by a consumer testing organization reports that at 95% confidence he has determined that the true average content of the Uncola soft drinks is between 11.9 to 12.1 ounces. He further reports that his sample revealed an average content of 12 ounces, but he forgot to report the size of the sample he had selected. Assuming the standard deviation of the population is 0.5, determine the size of the sample.

## How probability relates to real-world.

Read the article “Medical False Positives and False Negatives”: https://brownmath.com/stat/falsepos.htm
Write a response to the following discussion question in the Discussion forum:

Explain what conditional probability means and how it is applied to the study in the article.
Explain your thoughts regarding this study. Does this study validate the need to understand probability and how probability relates to real-world examples? Why?

Note. Initial answers to the discussion question must be substantive and in the range of 250-400 words. Any references used should be properly cited following APA formatting guidelines.

## Relationship between variables.

When studying the relationship between two variables, we are looking for an association between them. An explanatory variable is the “input” variable and the response variable is the “output” variable. What is the explanatory variable for this study? What is the response variable?
What is a possible conclusion based on the graph?
A lurking variable is a variable that is not included in a statistical analysis, but may affect the relationship between the explanatory and response variables. It can falsely identify a strong relationship between variables or hide the true relationship. What are possible lurking variables for this study?

## What is a point estimate?

Question 1
The following shows the temperatures (high, low) and weather conditions in a given Sunday for some selected world cities. For the weather conditions, the following notations are used: c = clear; cl = cloudy; sh = showers; pc = partly cloudy.

1. What is an element? How many elements are in this data set? Name one.
2. What is a variable? How many variables are in this data set? Name one.
3. What is an observation? How many observations are in this data set?  Name one.
4. Name the variables and indicate whether they are categorical or quantitative.

Question 2
A student has completed 20 courses in the School of Arts and Sciences. Her grades in the 20 courses are shown below.

1. Develop a frequency distribution table for the grades.
2. Create a pie graph and a bar chart for her grades.  Make sure that graphs have titles, labels, and keys.
3. Which graph or chart from #2 better represents the data? Why?

Question 3
The number of hours worked per week for a sample of ten students is shown below.

1. The median is the “middle number” in a set. When a set has an even number of data points, you are supposed to average the middle two numbers to get the median. Explain why a student who averages 22 and 40 would get this problem wrong.  What is the real median?
2. What is the mode of the above data? What does it signify?
3. What is the mean number of hours worked?
4. Mean, median, and mode are all measures of central tendency. Compare the mean, median, and the mode for this data set. Which one is the best representative of the number of hours worked?  Why?

Question 4
You are given the following information on Events A, B, C, and D.

1. Compute P(D).  Use the Addition formula.
2. Compute P(A ∩ B).  Use the Conditional Probability Formula.
3. Compute P(A | C).
4. What is a complement? Compute the probability of the complement of C.
5. The probability of getting a raise higher than the cost of living in company ABC is 0.30.  The probability of getting a raise higher than the cost of living given that it is  Monday in company ABC is 0.30.  Are these events independent, or dependent, and why?
6. When two events are mutually exclusive, will there be an intersection of data?  Why or why not?

Question 5
1. When a particular machine is functioning properly, 80% of the items produced are non-defective. If five items are examined, what is the probability that exactly two are defective?

Question 6
The average starting salary of this year’s graduates of a large university (LU) is \$60,000 with a standard deviation of \$5,000. Furthermore, it is known that the starting salaries are normally distributed.
1. What is the probability that a randomly selected LU graduate will have a starting salary of at least \$66,000?
2. Individuals with starting salaries of less than \$45,000 receive a free class. What percentage of the graduates will receive a free class?
3. According to the textbook, what percentage of values fall one standard deviation from the mean?  Two standard deviations from the mean?
4. What are the minimum and the maximum starting salaries of the middle 95.4% of the LU graduates?

Question 7
A simple random sample of 7 computer programmers in Houston, Texas revealed the sex of the programmers and the following information about their weekly incomes.

G                          280                      F
1. What is a point estimate?  (define it)
2. What is the point estimate for the average weekly income of all the computer programmers in Houston?
3. Determine a point estimate for the proportion of all programmers in Houston who are female.

Question 8
Students of a large university spend an average of \$6 a day on lunch. The standard deviation of the expenditure is \$2. A simple random sample of 81 students is taken.
1. What is the probability that the sample mean will be at least \$5.25?
2. What is the probability that the sample mean will be at least \$6.50?
3. What is the range of money spent by people who fall within one standard deviation of the mean?
4. Kelsey spent \$12 on her lunch today.  Explain to her, in terms of the normal distribution curve and standard deviation, why her purchase is not very typical.

## Degrees of freedom between persons, Sum of squares between persons,and Mean square between persons.

Statistics Exercise IV

These weekly exercises provide the opportunity for you to understand and apply statistical methods and analysis.

#1.  Define the following terms:

Sum of squares between groups
Sum of squares error
Mean square between groups
Mean square error

#2.  Define the following terms:

Degrees of freedom between persons
Sum of squares between persons
Mean square between persons

#3.  Explain why the critical value can be different for each hypothesis test computed using the two-way between-subjects ANOVA.

Use SPSS and the data file found in syllabus resources (DATA540.SAV) to answer the following questions.  Round your answers to the nearest dollar, percentage point, or whole number.

#4.  Perform a chi-square test to look at the relationship between region of the country (REGION) and financial comfort (FCOMFORT).  Using alpha = .05, what would you conclude from your test:A.Financial comfort differs depending on the area one lives in. B.People living in less expensive areas are more likely to report that they are financially comfortable. C.There is not a significant relationship between region and financial comfort. D.People living in the northeast region are most likely to report that they are financially struggling.

#5.  Perform a one-way ANOVA to look at whether income (INC1) differs by type of relationship (RELAT).  Which of the following describes your result:A.F(3,396) = 4.91, p > .05 B.F(3,396) = 4.91, p < .001. C.F(3,396) = 6.85, p > .05 D.F(3,396) = 6.85, p < .001 Perform a 2-way ANOVA with participant’s income (INC1) as the dependent variable and with gender (GENDER1) and          marital status (MSTAT) as independent variables. Interpret your results in questions 6, 7 and 8. (Hint: click the “Plots” button in the Univariate routine to create a graph). #6.  The main effect due to gender indicates that:A.Women earn more than men. B.Men earn more than women. C.Men and women have incomes that are not significantly different. D.Participants earn more than their partners. #7.  The main effect due to marital status indicates:A.Your income tends to decrease after a divorce. B.Getting married tends to increase your income. C.Marital status is unrelated to income. D.Married people tend to earn more than single people. #8.  The interaction effect indicates:A.Men earn more than women and married people earn more than singles. B.The male/female income difference is greater when comparing married people than when comparing singles. C.The interaction effect is non-significant. D.Marriage helps men’s careers more than it helps women’s careers.

## Describe how organizations use statistical thinking to be more competitive.

Ben Davis had just completed an intensive course in Statistical Thinking for Business Improvement, which was offered to all employees of a large health maintenance organization. There was no time to celebrate, however, because he was already under a lot of pressure. Ben works as a pharmacist’s assistant in the HMO’s pharmacy, and his manager, Juan de Pacotilla, was about to be fired. Juan’s dismissal appeared to be imminent due to numerous complaints, and even a few lawsuits over inaccurate prescriptions. Juan now was asking Ben for his assistance in trying to resolve the problem, preferably yesterday!

“Ben, I really need your help! If I can’t show some major improvement or at least a solid plan by next month, I’m history.”
“I’ll be glad to help, Juan, but what can I do? I’m just a pharmacist’s assistant.”
“I don’t care what your job title is; I think you’re just the person who can get this done. I realize I’ve been too far removed from day-to-day operations in the pharmacy, but you work there every day. You’re in a much better position to find out how to fix the problem. Just tell me what to do, and I’ll do it.”
“But what about the statistical consultant you hired to analyze the data on inaccurate prescriptions?”
“Ben, to be honest, I’m really disappointed with that guy. He has spent two weeks trying to come up with a new modeling approach to predict weekly inaccurate prescriptions. I tried to explain to him that I don’t want to predict the mistakes, I want to eliminate them! I don’t think I got through, however, because he said we need a month of additional data to verify the model, and then he can apply a new method he just read about in a journal to identify ‘change points in the time series,’ whatever that means. But get this, he will only identify the change points and send me a list; he says it’s my job to figure out what they mean and how to respond. I don’t know much about statistics — the only thing I remember from my course in college is that it was the worst course I ever took– but I’m becoming convinced that it actually doesn’t have much to offer in solving real problems. You’ve just gone through this statistical thinking course, though, so maybe you can see something I can’t. To me, statistical thinking sounds like an oxymoron. I realize it’s a long shot, but I was hoping you could use this as the project you need to officially complete the course.”

“I see your point, Juan. I felt the same way, too. This course was interesting, though, because it didn’t focus on crunching numbers. I have some ideas about how we can approach making improvements in prescription accuracy, and I think this would be a great project. We may not be able to solve it ourselves, however. As you know, there is a lot of finger-pointing going on; the pharmacists blame sloppy handwriting and incomplete instructions from doctors for the problem; doctors blame pharmacy assistants like me who actually do most of the computer entry of the prescriptions, claiming that we are incompetent; and the assistants tend to blame the pharmacists for assuming too much about our knowledge of medical terminology, brand names, known drug interactions, and so on.”
“It sounds like there’s no hope, Ben!”

“I wouldn’t say that at all, Juan. It’s just that there may be no quick fix we can do by ourselves in the pharmacy. Let me explain how I’m thinking about this and how I would propose attacking the problem using what I just learned in the statistical thinking course.”

Source: G. C. Britz, D. W. Emerling, L. B. Hare, R. W. Hoerl, & J. E. Shade. “How to Teach Others to Apply Statistical Thinking.” Quality Progress (June 1997): 67–80.

Assuming the role of Ben Davis, write a three to four (3-4) page paper in which you apply the approach discussed in the textbook to this problem. You’ll have to make some assumptions about the processes used by the HMO pharmacy. Also, please use the Internet and / or Strayer LRC to research articles on common problems or errors that pharmacies face. Your paper should address the following points:
1. Develop a process map about the prescription filling process for HMO’s pharmacy, in which you specify the key problems that the HMO’s pharmacy might be experiencing. Next, use the supplier, input, process steps, output, and customer (SIPOC) model to analyze the HMO pharmacy’s business process.
2. Analyze the process map and SIPOC model to identify possible main root causes of the problems. Next, categorize whether the main root causes of the problem are special causes or common causes. Provide a rationale for your response.
3. Suggest the main tools that you would use and the data that you would collect in order to analyze the business process and correct the problem. Justify your response.
4. Propose one (1) solution to the HMO pharmacy’s on-going problem(s) and propose one (1) strategy to measure the aforementioned solution. Provide a rationale for your response.
5. Use at least two (2) quality references. Note: Wikipedia and other Websites do not qualify as academic resources.
Your assignment must follow these formatting requirements:Be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides; citations and references must follow APA format. Check with your professor for any additional instructions.Include a cover page containing the title of the assignment, the student’s name, the professor’s name, the course title, and the date. The cover page and the reference page are not included in the required assignment page length.The specific course learning outcomes associated with this assignment are:Describe how organizations use statistical thinking to be more competitive.
Apply the basic principles of statistical thinking to business processes.Apply the SIPOC model to identify OFIs in business processes.Use technology and information resources to research issues in business process improvement.Write clearly and concisely about business process improvement using proper writing mechanics.

## Explain what components are needed in the introduction to a survey to address ethical concerns.

Part 1: Ethics in Research
Choose 1 example of unethical research in a business setting, and discuss the following:

Explain why research might be considered unethical.
Explain what ethical considerations there are and how to avoid these issues in your research project.
Explain what components are needed in the introduction to a survey to address ethical concerns.

You may wish to review an example time line by clicking here.

Part 2: Preparing to Create Your Survey
Building on the organizational issue, problem, or topic that you identified in Unit 1, complete the following:

Write 1 research question regarding that topic.