Statistics Concepts and Descriptive Measures

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Statistics Concepts and Descriptive Measures
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The purpose of this assignment to orient students to the key concepts in statistics. This assignment will introduce students to the language of statistics. Students will also get a chance to warm-up on evaluating some basic descriptive statistics using Excel® prior to the course start.
Assignment Steps
This assignment has an Excel® dataset spreadsheet attached. You will be required to only do one of the three datasets.
Resource: Microsoft Excel®, Statistics Concepts and Descriptive Measures Data Set
Download the Statistics Concepts and Descriptive Measures Data Set.
Choose one of the following datasets to complete this assignment:
Consumer Food Financial Hospital Answer each of the following in a total of 90 words:
For each column, identify whether the data is qualitative or quantitative. Identify the level of measurement for the data in each column. For each column containing quantitative data: Evaluate the mean and median Interpret the mean and median in plain non-technical terms Use the Excel =AVERAGE function to find the mean Use the Excel =MEDIAN function to find the median For each column containing quantitative data: Evaluate the standard deviation and range Interpret the standard deviation and range in plain non-technical terms Use the Excel =STDEV.S function to find the standard deviation For range (maximum value minus the minimum value), find the maximum value using the Excel =MAX function and find the minimum value using the Excel’s =MIN function Click the Assignment Files tab to submit your assignment.

 

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How is Poisson distribution related to Exponential distribution?

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2 QUESTIONS PROBABILITY AND STATISTICS
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1. How is Poisson distribution related to Exponential distribution? In other words, if an event follows Poisson distribution what other even would have to follow the exponential distribution?

2. In excel, plot the PMF/PDFand CDF of Poisson, Exponential, and Normal distributions as a function of their parameters (Lambda for Poisson and Exponential – mean and variance for Normal).

a. Determine initial values for X: To do this first generate equally spaced numbers between 0 and 10 (or more if you prefer).
b. Define initial values for parameters: Then use a separate cell with proper name to enter the initial value for parameters:
i. Lambda=1 for Poisson and Exponential(choose arbitrary initial values if you have more than one parameter; more than one parameter is possible depending on the formula you use).
ii. Mean=1 & variance=2 for Normal
c. Create three sheets: Copy the worksheet twice so you can plot each distribution separately. Name the resulting three worksheets according to the distribution you are plotting inside them.
d. Calculate using excel formulas: Then, in each of the three sheets, calculate the requested values(PDF, PMF, CDF) using excel formulas (you must use excel formulas, instead of calculating things outside).
e. Plot: Use a scatter plot (or other plotting methods that you prefer) to plot two-dimensional graphs for PDF, PMF, and CDFs. Give your graphs and its axes proper names. You should now have 6 graphs – two for each distribution.
f. Now make a copy of each worksheet, and increase the lambda value (first play with different values but ultimately set Lambda to 4). Explain how the distribution changes as lambda increases?

3. In semi-conductor manufacturing process, the maximum number of defects that we can accept on a wafer is 5. If the number of defects on a circuit follows a Poisson distribution with a mean of 2,
a. What is the probability that we reject a circuit? write the formula, write the value of each parameter (e.g. lambda), then provide the final value (no need to show the calculation steps; if you correctly write the value of parameters in the beginning you can only list the final value).

b. What percentage of circuits will be rejected in each lot?in each day? In each week?

c. On average, how many acceptable wafers do we make before we make an unacceptable wafer?

d. Imagine we can purchase a better machine that produces an average of 1 defect per wafer. Using the new machine, what percentage of each production batch will be unacceptable?

e. If the machine costs $1M and each unacceptable product costs us $200. At what level of production, would the investment in the new machine pay-off? How should the managers decide whether they should purchase the machine or not?

 

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. Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 85% claim the company is making?

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Advanced Statistics – 5 questions (Proportions)
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Question 1:
A hypothesis test is conducted with a significance level of 10%. The alternative hypothesis states that more than 15% of a population has at least one sibling. The p-value for the test is calculated to be 0.27. Which statement is correct?

a. We can conclude that more than 27% of the population has at least one sibling.
b. We can conclude that exactly 27% of the population has at least one sibling.
c. We can conclude that more than 15% of the population has at least one sibling.
d. We cannot conclude that more than 15% of the population has at least one sibling.
e. There is not enough information given to make a conclusion.

Question 2:
Big Sweets candy company is testing one of its machines in the factory to make sure it is producing more than 96% high-quality candy (H0: p = 0.96; Ha: p > 0.96; α = 0.05). The test results in a p-value of 0.12. However, the company is unaware that it is actually producing 98% high-quality candy. What MOST likely happens as a result of the testing?

a. The company rejects H0, making a Type I error.
b. The company fails to reject H0, making a Type I error.
c. The company rejects H0, making a Type II error.
d. The company fails to reject H0, making a Type II error.
e. The company rejects H0 correctly.

Question 3:
A large school district notices that about 26% of its sophomore students fail Algebra I. An online education supplier suggests the district try its new technology software, which is designed to improve Algebra 1 skills and, thus, decrease the number of students who fail the course. The new technology software is quite expensive, so the company offers a free, one-year trial period to determine whether the Algebra 1 pass rate improves. If it works, the district will pay for continued use of the software. What would happen if the school district makes a Type I error?
a. Claim the new technology software decreases the number of students who fail Algebra 1, when it does decrease the number.
b. Claim the new technology software decreases the number of students who fail Algebra 1, when it does not decrease the number.
c. Claim the new technology software does not decrease the number of students who fail Algebra 1, when it does decrease the number.
d. Claim the new technology software does not decrease the number of students who fail Algebra 1, when it does not decrease the number.
e. Claim the new technology software increases the number of students who fail Algebra 1, when it decreases the number.

Question 4:

A large restaurant is being sued for age discrimination because 15% of newly hired candidates are between the ages of 30 years and 50 years when 50% of all applicants were in that age bracket. You plan to use hypothesis testing to determine whether there is significant evidence that the company’s hiring practices are discriminatory.

Part A: State the null and alternative hypotheses for the significance test. (2 points)

Part B: In the context of the problem, what would a Type I error be? A Type II error? (2 points)

Part C: If the hypothesis is tested at a 1% level of significance instead of 5%, how will this affect the power of the test? (3 points)

Part D: If the hypothesis is tested based on the hiring of 1,000 employees rather than 100 employees, how will this affect the power of the test? (3 points)

Question 5:
A manufacturer of a new medication on the market for Crohn’s disease makes a claim that the medication is effective in 85% of people who have the disease. One hundred seventy-five individuals with Crohn’s disease are given the medication, and 135 of them note the medication was effective. Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 85% claim the company is making? Make sure to include parameter, conditions, calculations, and a conclusion in your answer.

 

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Plot the probability mass function (PMF) and the cumulative distribution function (CDF) of 3 random variables

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GENG 200 Probability and Statistics Computer Based Assignment #2 2
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Probability Exercise # 1:
Collect and Comment on the variability of three recent data sets describing similar processes
(could be prices of three items over the last month, demographic information related to 3 countries overlast year, etc.).
Probability Exercise # 2:
Plot the probability mass function (PMF) and the cumulative distribution function (CDF) of 3 random variables following (1) binomial distribution [p,n], (
2) a geometric distribution [p], and
(3) Poissondistribution [????].

instructions
You have to consider two sets of parameters per distribution which can be chosen arbitrarily.
The following steps can be followed:
Setp1: Establish two sets of parameters of the distribution: For Geometric and Poisson distributions take two values of p (p1 and p2) and take two values of [????], (????1 and ????2) respectively. For the binomial you should take two values of p and two values of n, first keep p fixed and change n, in the second keep n fixed and change p.
Step 2: Generate the random variables (at least 10 values) [column 1]Step 3: Calculate the PMF [column 2] and CDF [column 3]Step 4: Plot the PMF and CDF in different graphics (It is recommended to combine the graphics while changing the parameters).Comment on how the parameters values affect the distribution

 

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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.

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Statistics Homework
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Read the following case study.
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.

 

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“Auto Insurance Costs: Where Does Your State Rank?”

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Statistics : 1
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Statistician Nate Silver became famous in 2008 when he correctly predicted the Presidential Election in 49 of the 50 states. Mr. Silver has done more than just predicting elections. Visit Nate Silver’s blog, located at https://fivethirtyeight.com/, and read one blog entry that is related to one of this week’s topics. • From the activity, summarize the blog entry that you have read. Next, explain the manner in which Nate Silver’s analysis in your chosen blog entry addresses the salient points of one particular topic related to this class. • H.G. Wells once said, “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write!” Take a position on whether you agree or disagree with this statement, and provide a rationale for your response.
Visit one of the following newspapers’ websites: Wall Street Journal, Washington Post, USA Today, or New York Times. Select a line graph, pie chart, or bar chart on the website. • From the activity, discuss the data that the graph is used to visually represent. Speculate on why the editor chose the graph, as opposed to merely reporting the data. Read the article titled, “Auto Insurance Costs: Where Does Your State Rank?” https://www.cbsnews.com/news/auto-insurance-costs-where-does-your-state-rank/ • From the activity, the table shows Average Insurance Costs by State. Select two (2) states that are of interest to you. Next, speculate on three (3) possible reasons why the states you have chosen would have a difference in average insurance costs. • From the activity, select ten (10) states and calculate the mean and standard deviation for average insurance costs. Next, calculate the mean and standard deviation for average insurance costs for all 51 states (including Washington, D.C.). Compare and contrast the means and standard deviations for the ten (10) states you selected and all 51 states.

 

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Create a research question in the field of psychology that you are interested in researching.

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Statistics:Psychology
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In 1,250-1,500 words, answer the following questions about possible research options.
Create a research question in the field of psychology that you are interested in researching. Write questions clearly. Include a brief background of the problem you are proposing and why it is important to the field of psychology.
State the null and alternative hypothesis (in both words and statistical notation) need to address the research question.
Choose which statistical test would be used to conduct the study and support it with research.
Describe the type of data needs to be collected to conduct the study and what techniques are best for collecting data.
Use three to five scholarly resources to support your explanations.

 

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create a dataset for a hypothetical repeated-measures experimental design.

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Statistics SPSS Assignment
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You will submit one Word document for this activity. You will create this Word document by cutting and pasting SPSS output into Word.

This assignment consists of two parts. In the first part, you will utilize an existing dataset to analyze the dataset from repeated-measures experimental design. All SPSS output should be pasted into your Word document. In the second part, you will be asked to create a dataset for a hypothetical repeated-measures experimental design. Finally, you will answer questions about your hypothetical dataset.

Part A. SPSS Assignment
The “Activity 6.sav” file contains a dataset of a high school teacher interested in determining whether his students’ test scores increase over the course of a 12 week period. In the dataset, you will find the following variables:
Participant: unique identifier
Gender: Male (M) or Female (F)
Score_0 – score on the initial course pre-test (first day of class)
Score_2 – score at the end of week 2
Score_4 – score at the end of week 4
Score_6 – score at the end of week 6
Score_8 – score at the end of week 8
Score_10 – score at the end of week 10
Score_12 – score at the end of the course (week 12)

To complete this Activity
1. Exploratory Data Analysis.
a. Perform exploratory data analysis on the relevant variables in the dataset. When possible, include appropriate graphs to help illustrate the dataset.
b. Compose a one to two paragraph write up of the data.
c. Create an APA style table that presents descriptive statistics for the sample.
2. Repeated-Measures ANOVA. Perform a repeated-measures ANOVA using the “Activity 6.sav” data set. You will use Score_0 through Score_12 as your repeated measure (7 levels), and gender as a fixed factor.
a. Is the assumption of sphericity violated? How can you tell? What does this mean in the context of interpreting the results?
b. Is there a main effect of gender? If so, explain the effect. Use post hoc tests when necessary or explain why they are not required in this specific case.
c. Is there a main effect time (i.e., an increase in scores from Week 0 to Week 12)? If so, explain the effect. Use post hoc tests when necessary or explain why they are not required in this specific case. Examine the output carefully and give as much detail as possible in your findings.
d. Write up the results in APA style and interpret them. Be sure that you discuss both main effects and the presence/absence of an interaction between the two.
Part B. Applying Analytical Strategies to an Area of Research Interest
3. Briefly restate your research area of interest.
a. Identify at least 2 variables for which you would utilize a repeated-measures ANOVA in your analysis. Describe the variables and their scale of measurement. Identify whether each factor is fixed or repeating. Where on the SPSS output would you look to find out if you violated the assumption of sphericity? If the data did violate this assumption, what would the impact be on your analysis?

 

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Inferential Statistics Analysis and Writeup

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Assignment #3: Inferential Statistics Analysis and Writeup
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Purpose: The purpose of this assignment is to develop and carry out an inferential statistics analysis plan and write up the findings. There are two main parts to this assignment: ● Part A: Inferential Statistics Data Plan and Analysis ● Part B: Write up of Results Part A: Prepare Data Plan, Analyze Data, and Complete Part A of the Assignment #3 Template ➢ Task 1: Select Variables. Review the variables you used for assignments #1 and #2. Select your qualitative socioeconomic variable as your grouping variable and the two expenditure variables from the variables used in these previous assignments. Fill in Table 1: Variables Selected for Analysis with name, description, and type of variable (i.e., qualitative or quantitative). ➢ Task 2: Select and Run a One Sample Confidence Interval Analysis. For one expenditure variable, select and run the appropriate method for estimating a parameter, based on a statistic (i.e., confidence interval method). Complete Table 2: Confidence Interval Information and Results, which follows the format outlined by Kozak and the course’s problem-solving approach, including: ○ Random variable stated in words ○ Confidence interval method, including rationale and assumptions ○ Method used for analyzing data (i.e., web applets, Excel, TI calculator, etc.). ○ Results obtained ○ Interpretation ➢ Task 3: Select Two Sample Hypothesis Test. Using the second expenditure variable (with the socioeconomic variable as the grouping variable), select and run the appropriate method for making decisions about two parameters relative to observed statistics (i.e., two sample STAT200: Assignment #3 – Inferential Statistics Analysis and Writeup – Instructions Page 2 of 5 hypothesis test method). Complete Table 3: Two Sample Hypothesis Test Analysis, which follows the format outlined by Kozak and the course’s problem-solving approach, including: ○ Hypotheses (null and alternative). ○ Two sample hypothesis testing method, including rationale and assumptions ○ Method used for analyzing data (i.e., web applets, Excel, TI calculator, etc.). ○ Results obtained. ○ Interpretation (i.e., Reject the null hypothesis OR Fail to reject null hypothesis) Step 2: Write Up Results and Complete Part B of the Assignment #3 Template For this 1 to 2 page section, refer to the inferential statistics data plan and computations done for Part A of this assignment. Address the following area: ➢ Introduction. Based on the scenario you submitted for the second assignment, provide a brief description of scenario, including the variables that were used in this analysis. Include a completed “Table 1: Variables Selected for Analysis to show the variables you selected for analysis. ➢ Data Set Description and Method Used for Analysis. Briefly describe the data set, using information provided with data set and write up in Assignment #2. Also describe what method(s) (i.e., free web applets, Excel, TI Calculator) you used to analyze the data. ➢ Results. In this section, you will report the results of your inferential statistics data analysis.

 

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