Develop a null and an alternative hypothesis for a decision that is relevant to your life.

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Alternative hypotheses

Develop a null and an alternative hypothesis for a decision that is relevant to your life. This decision can be personal or professional. Share your null and alternative hypotheses with your peers in this week’s discussion. Be sure to include the following in your post.Define/discuss:

All variables ;

The appropriate test statistic, and if it is a one- or two-tailed test;

Your selection process;

The Type I and Type II errors that could occur with your decision‐making process; and

Your proposed next steps based on your results.

Be sure to include 2 references to support your findings.

 

Show that the conditional distribution of belongs to the .potential family of dis,distributions. Find the canonical parameter. Hence find the mean and the ValiSaCe of y1.

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Generalized linear models

  1. a) Let Y b bit y ma® unction 1(.6)=vV),0—OK where r is known. Show that the distribution belongs to the exponential family and hence find the mean sad VBSIBBOP of y. b) Cns.’ r a 2 x 2 contingency table with one margin fixed at n, and n, binomial(n, ) (1 — u,binomial(n,,P,) _ P,(1

The conditional distribution of y, given = n d 71, (fluter = urFu.,) is..

Show that the conditional distribution of belongs to the .potential family of dis,distributions. Find the canonical parameter. Hence find the mean and the ValiSaCe of y1.

 

Calculate the average number of claims on any given day, week and month. Let t’ > 0 be an instance of time. Calculate the probability that at least one claim occurs within 5 days after t’. Calculate also the probability that at least 2 claims occur within 5 days after t’.

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Poisson process

An insurance company has an initial surplus of 100 and premium loading factor of 20%. Assume that claims arrive according to a Poisson process with parameter A = 5 and the size of claims Xi are iid random variables with Xi ,-,, exp( 1-0). The time unit is 1 week. Assume that 1 month is 4 weeks.

(a) Calculate the average number of claims on any given day, week and month. Let t’ > 0 be an instance of time. Calculate the probability that at least one claim occurs within 5 days after t’. Calculate also the probability that at least 2 claims occur within 5 days after t’.

(b) Let t = 2 months. Calculate the mean and variance of S(t) and of U(t), where (S(r)),>0 and (U(r)),>0 are the aggregate claim process and the surplus process of the described model.

(c) Derive an upper bound for the ultimate ruin probability using Lundberg’s inequality.

 

Develop tables for each of the statistical test in your study. Apply Linear regression, correlation, descriptive statistics and hypothesis testing to your primary data.

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Factors that impact mental health in the United States

  1. Develop tables for each of the statistical test in your study.
  2. Apply Linear regression, correlation, descriptive statistics and hypothesis testing to your primary data.
  3. Each table must be labeled with a review of the results underneath the table.
  4. Strongly suggest that students assign a test to each member of the group for full participation.

 

Draw the residual plots against each significant predictor, and output variable. Interpret the results of the plots. Describe any problem or issue of the above regression model and explain how to improve the regression model.

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Part 1-Python Programming

  • Submit your codes and outputs in a readable format (Word, HTML, Text, or PDF file) for full credits!

Multiple Linear Regression Analysis

1) Download the file ‘bmi’ in the homework folder of the Course Blackboard Read in the file and display the first 5 observations

2) Draw the histograms and pairwise scatter plots of all numeric columns using seaborn pairplot.

3) Check the pairwise correlation coefficients between variables. Interpret the result and state which variables have significant linear relationships with ‘BodyFatSiriEqu’.

4) Use ‘BodyFatSiriEqu’ as output variable and all other columns as input variables to Develop a regression model. Write the regression model equation.

5) Identify all significant coefficients of predictors at α=0.05 level using t-tests.

6) Interpret the meaning of coefficients. Compare and interpret the regression model to the result of the pairwise correlation coefficients in (c).

7) Remove insignificant predictors from (e) and develop a regression model with remaining significant input variables. Write the regression model equation. Compare and interpret the regression models from (d) and (f)

8) Test the overall model using F-test of the regression output in (f). Interpret the result of the test.

9) State the goodness-of-fit of the regression model

10) Draw the residual plots against each significant predictor, and output variable. Interpret the results of the plots.

11) Describe any problem or issue of the above regression model and explain how to improve the regression model.

 

.

 

What are the parameters of interest? Are the assumptions satisfied? What are the hypotheses? What is the formula for the test statistic, and the distribution for the test statistic?

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Testing for independence

Lab Instructions: In this lab, we will begin to develop the concepts found on testing for independence in chapter 6, section 4.  be sure to:

Follow all instructions.

Answer each question completely.

Include JMP output to help demonstrate and support your answers.

Submission Instructions: You will be submitting your lab in Gradescope. Save the file for the lab and upload with the title Math539 _LabXX_Name. Be sure to input your lab section and name into the title of the file.

Step 1: Data Collection

Complete the survey in the pre-assignment. Make sure that the data is in the correct form for JMP.

Step 2: Conduct the analysis

(3.75 pts.) Using the data, complete the following chart. You may combine categories so that the cells have at least 5 in each.

Ketchup Mustard Relish Mayonnaise Total

Male

Female

Total

Conduct a hypothesis test to determine if the factors are independent:

(2 pts.) What are the parameters of interest?

(2 pts.) Are the assumptions satisfied?

(1 pt.) What are the hypotheses?

(2 pts.) What is the formula for the test statistic, and the distribution for the test statistic? Be sure to include the degrees of freedom.

(5 pts.) Calculate the test statistic. You may want to create a table such as the one below in Excel. Please include all work and/or table.

Gender Favorite Snack Observed Expected Difference Square Ratio

(1 pt.) Find the p-value using the chi-squared table to estimate it.

(1 pt.) State your decision.

(1 pt.) State your conclusion.

(2 pts.) Conduct the analysis in JMP. Compare answers. Are they the same? Please include the JMP output.

 

What would be the defining relationship and generator in this design? Calculate the main effect of A manually. Enter the data to Minitab and analyze the data and make conclusions.

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ISE 135 In-class exercise (Groups of max. 3 students)

Fractional Factorial Design

You need to answer the following questions and submit a word document to CANVAS with your answers

Consider a 25-1 design below. Note that Basic design is already created using 24 runs.

Create the 5th column

What would be the defining relationship and generator in this design? . Minitab will also tell you what the generator of this /1/2 fractional design of 25 experiment once you create the design.

Calculate the main effect of A manually.

Enter the data to Minitab and analyze the data and make conclusions. Be careful- this is a single replicate, so you need to do some extra steps to create an ANOVA table.

If your aim was to find the best combination of factor levels that maximize your response, what would they be?

Basic Design Treatment Combination Yield

Run A B C D E

1 – – – – e 8

2 + – – – a 9

3 – + – – b 34

4 + + – – abe 52

5 – – + – c 16

6 + – + – ace 22

7 – + + – bce 45

8 + + + – abc 60

9 – – – + d 6

10 + – – + ade 10

11 – + – + bde 30

12 + + – + abd 50

13 – – + + cde 15

14 + – + + acd 21

15 – + + + bcd 44

16 + + + + abcde 63

 

Construct a confidence interval for the difference of the two means using the method described in class for normal data with different variances.

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Assignment 5 Confidence intervals

Show all work, when statkey is used, include a screenprint of your output. If you do not include the screenprint it counts as not working the problem.

1: The data for this problem is in ques1.csv in canvas

Download the data to your computer and upload it to statkey, bootstrap confidence intervals for a mean.

  1. What is the mean of the data
  2. What is the standard deviation of the data
  3. Calculate a t interval for the mean
  4. What is a bootstrap confidence interval for the mean
  5. If I tell you that the data is Poisson, calculate the confidence interval for lambda using the normal approximation.
  6. Using the fact that the data is Poisson calculate the confidence interval for the standard deviation.

The data for this is in ques2.csv, There are 10 measurements in the data set from the first sample, with mean 6.8 and variance 12.84. There are 20 measurements from the second data set with mean 10.5 and variance 14.68.

  1. Construct a confidence interval for the difference of the two means using the method described in class for normal data with different variances.
  2. Construct a confidence interval for the difference of the two means using the method described in class for normal data with the same variances.
  3. Construct a bootstrap confidence interval for the difference in means.
  4. Construct a confidence interval for the difference in means use the normal approximation when we assume both samples are from Poisson distributions.

 

Suppose

𝑥𝑥𝑖𝑖 𝑖𝑖 = 1, … , 𝑛𝑛 𝑖𝑖𝑖𝑖 𝑑𝑑𝑖𝑖𝑖𝑖𝑠𝑠𝑠𝑠𝑖𝑖𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑑𝑑 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑠𝑠𝑑𝑑𝑖𝑖𝑛𝑛𝑎𝑎 𝑠𝑠𝑎𝑎 𝑠𝑠ℎ𝑠𝑠 𝑑𝑑𝑖𝑖𝑖𝑖𝑠𝑠𝑠𝑠𝑖𝑖𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖𝑎𝑎𝑛𝑛 𝑤𝑤𝑖𝑖𝑠𝑠ℎ 𝑑𝑑𝑠𝑠𝑛𝑛𝑖𝑖𝑖𝑖𝑠𝑠𝑑𝑑 12 𝑠𝑠𝑥𝑥𝑒𝑒(−|𝑥𝑥𝑖𝑖 − 𝜇𝜇|)

What is the maximum likelihood estimate of 𝜇𝜇? Note 𝑠𝑠𝑥𝑥𝑒𝑒(𝑧𝑧) = 𝑠𝑠𝑧𝑧 HINT what is the derivative with respect to z of |𝑧𝑧| when z is positive, when z is negative???

 

 

 

What are the data used and how the data have been collected? 2. How the data have been processed to derive the Happiness Index? What are the limitations of the entire process?

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Happiness Index

Visit the Happiness Index website, explore, and write a report based on the data provided on the website. The paper must address the following issues:

  1. What are the data used and how the data have been collected? 2. How the data have been processed to derive the Happiness Index?
  2. What are the limitations of the entire process?
  3. What can you learn from this website?

Format

  • Introduction: in brief discussion on the Happiness Index.
  • Body: Discuss the issues from above.
  • Conclusion: Conclude the theme of the findings from the entire paper. APA style paper and referencing Word Limit: 3,000 words (± 10%), equivalent to 10 pages excluding cover, executive summary, contents, and appendix.

Tips: • Focus on Chapters 1 and 2 for understanding the Happiness Index.

  • Focus on two main data sets, i.e., life evaluation date and life factors.

 

If one eco-car is randomly selected from this population, what is the probability the fuel efficiency will be at least 31.13? If 10 of these eco-cars are randomly selected from this population, what is the probability the mean MPG will be between 30.12 mpg and 32.27 mpg?

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ASSIGNMENT

FILL OUT ESSAY box with complete and full solution as shown in the applicable class lecture video(s). Do this solution without any need of calculating a Z-score, must be done without that step and students are prohibited from using any standard normal table. No file upload option allowed, must type out solution in the text box provided.

Given: MPG (mile per gallon Fuel efficiency) of a certain model eco-car is normally distributed with mean of 31.1 and standard deviation of 1.245.

Round answers to nearest thousandth and keep in decimal format. Give full solution for each of these parts (and note the start to Part A, versus the start of Part B, please) in this ESSAY box formatted question.

Part A: If one eco-car is randomly selected from this population, what is the probability the fuel efficiency will be at least 31.13? (re-read directions to make sure your typed solution is complete).

Part B: If 10 of these eco-cars are randomly selected from this population, what is the probability the mean MPG will be between 30.12 mpg and 32.27 mpg? (re-read directions to make sure your typed solution is very complete).