Mini Group Project 2 8W Fall 2023

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University of North Texas *

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5130

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Statistics

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Feb 20, 2024

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1 Mini-Group Project 2 (8W section Fall’23), Team ____ Instructions:  Follow the instructions provided in each task.  It is crucial that your responses are clear and written with no grammatical errors as this is a professional setting. Make sure to properly number your answers so that it is easy for the reader to follow your analysis.  You can whether use Microsoft Excel or R to complete the homework assignment. Some students are tempted to use Python to complete the work. Since the textbook provides instructions only with R and Excel, you can only use R or Excel to complete the mini-group projects.  There are three deliverables: The first two will be submitted on Canvas, the third one should be sent via email. (1) Use the provided MS Word template to enter your work, convert it to pdf, and name it as MGP2_Team_Number before submitting in Canvas. If you use Excel, you can copy and paste your work (charts/graphs) into this Word template and save as your document in pdf format before submitting in Canvas. If you use R, knit your Quarto document in pdf before submitting in Canvas. (2) Your Excel file (or the Quarto document if R is used) should show your work or codes for each Task. The Excel file should show the formulas used to derive the results. If you use R, make sure codes run with no error. (3) Signed statement of team member contribution form. Each team member of the project group should indicate their contribution to the project showcase and sign the Statement of Contribution Form. Group project grades will not be released without the signed statement of member contribution form. Have one group member to send this signed statement to levent.bulut@unt.edu and include each team member and the TA ( srinidhiyadavboda@my.unt.edu ) on the cc.  If you have any questions about the mini-group project tasks, use Week 7 discussion forum to post your questions. Good luck! Team ___ [Enter your Team number in her]

2 Mini-Group Project 2 (8W section Fall’23), Team ____ Data for Tasks 0, 1 and 2: In this project, we will work with two datasets. For Tasks 0, 1 and 2, we will use the Gallup Presidential Approval data for each President starting with Franklin D. Roosevelt. You can access the data from the following link: Presidential Job Approval--All Data | The American Presidency Project (ucsb.edu) . The data in this project is compiled based on responses to the survey question, "Do you approve or disapprove of the way [enter President name] is handling his job as President?" The Excel file contains public approval and disapproval ratings, as well as the proportion of respondents who answered "Don't know" or had no opinion. We will focus on a subset of data covering the last four presidents. The Gallup Job Approval data for the current President, Biden, is stored in the worksheet " Biden " and covers the period from January 21, 2021, to August 23, 2023. The data for President Trump is stored in the worksheet " Trump " and covers the period from January 20, 2017, to January 15, 2021. The data for President Obama is stored in the worksheet " Obama " and covers the period from January 19, 2009, to January 19, 2017. Finally, the data for President George W. Bush is stored in the worksheet " GWBush " and covers the period from February 1, 2001, to January 11, 2009. It's worth noting that the Presidential Job Approval rating data does not have the same frequency of dates for each presidential term. The data for President Biden is available on a monthly basis, while we have weekly data for the others. Data for Tasks 3,4, and 5: For Tasks 3, 4, and 5, we will use “PEW” worksheet. Team ___ [Enter your Team number in her] Data Description

3 Mini-Group Project 2 (8W section Fall’23), Team ____ In each worksheet dedicated to a President, populate the columns named "Approving_adj_[PresidentName]" and "Disapproving_adj_[PresidentName]". Allocate the value from the "Unsure/NoData" column between the "Approving" and "Disapproving" columns in a proportional manner. Ensure that the sum of "Approving_adj_[PresidentName]" and "Disapproving_adj_[PresidentName]" totals 100.  Order the Presidents in descending sequence based on the average "Approving_adj" ratings during their initial 1000 days in office along with their average "Approving_adj" values. Team ___ [Enter your Team number in her] Task 0 : Adjusting Presidential Approval Ratings

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4 Mini-Group Project 2 (8W section Fall’23), Team ____ You will use data in “Biden”, “Trump”, “Obama”, and “GWBush” worksheets to complete this task. a. Utilizing the given dataset, calculate a 95% confidence interval for the "Approving_adj" rate for each President. Keep in mind that this should be based on the adjusted Approval ratings you computed in Task 0. b. Identify which President has the narrowest and widest confidence intervals. Discuss potential factors, such as sample size or sample variance, that may influence these outcomes. Team ___ [Enter your Team number in her] Task 1 : Confidence Interval Estimations Task 2: Hypothesis Testing

5 Mini-Group Project 2 (8W section Fall’23), Team ____ You will use data in “Trump” and “Obama” worksheets to complete this task. In Task 2, you may find it necessary to filter the dataset for hypothesis testing purposes. a. Execute a t-test to examine whether President Obama had a higher approval rating during the initial 1000 days of his presidency compared to the final 1000 days. In your response, clearly outline the competing hypotheses, the calculated test statistics, and the p- value. Make sure to state your test conclusion unambiguously— either rejecting or failing to reject the null hypothesis—based on a 5% significance level. Also, clarify the criteria you employed to arrive at this conclusion. b. Perform a t-test to investigate if President Trump maintained a consistent approval rating between the first 500 days and the last 500 days of his term. Your answer should specify the competing hypotheses, the value of the test statistics, and the p-value. Clearly state the conclusion of your test, whether you reject or fail to reject the null hypothesis, at a 1% significance level. Explain the criteria that guided your conclusion. Team ___ [Enter your Team number in her]

6 Mini-Group Project 2 (8W section Fall’23), Team ____ By using the sex and Q3a variables in “PEW” worksheet, complete the following tasks: Research hypothesis: “Male Americans are more likely to prioritize having close relationship to Russia than their female counterparts” A. Clearly state both the null and alternative hypotheses. Null Hypothesis: Male Americans do not prioritize having a closer relationship with Russia than their female counterparts. Alternative hypothesis: Male Americans have prioritized having a closer relationship with Russia than their female counterparts. B. Differentiate between Type-I and Type-II errors in hypothesis testing. C. Assuming that the sampling distribution of the differences in sample proportions is approximately normal, construct a 90% confidence interval for the difference between the two population proportions (male and female). Provide an interpretation of your findings. D. Compute the value of the test statistics and the corresponding p- value, assuming a 5% significance level and independent sampling. Your calculation should focus on testing the difference between the two population proportions. E. Based on a 5% significance level, draw a conclusion from your test results. Do the findings lend support to the research hypothesis? Team ___ [Enter your Team number in her] Task 3: Statistical Inference Concerning Two populations

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7 Mini-Group Project 2 (8W section Fall’23), Team ____ You will use the partyln and Q4 variables in “PEW” worksheet to complete this task. In this task, we will test the public perception on a cold-era type relation with the US and China. Do you think the United States and China will one day confront like in the old days in between Cold-war era US-Russian relationship? Question 4 in the PEW dataset asks that question: Q4. How would you rate the likelihood of the current rivalry between China and the United States escalating into a confrontation resembling the Cold War? Just for the sake of this lab assignment, we want to test whether the political leanings (partyln) matters in this hypothetical scenario. In other words, we are interested in with the following research questions: “Are people with different political leanings equally likely to say conflict akin to the Cold War will occur between the China and the US?” Let us pretend that you are eager to know the answer and you will conduct a statistical analysis to test this research hypothesis by using PARTYLN and Q4 variables. A. Define the null and the alternative hypothesis. Team ___ [Enter your Team number in her] Task 4: Statistical Inference Concerning Two populations

8 Mini-Group Project 2 (8W section Fall’23), Team ____ B. Calculate the value of test statistics and the p-value at 8% significance level to test your hypothesis. C. At the 5% level of significance, what is your conclusion to the test. Do the results support the research hypothesis? Team ___ [Enter your Team number in her]

9 Mini-Group Project 2 (8W section Fall’23), Team ____ You will use the EDUCATION and PARTYLN variables in “PEW” worksheet to complete this task. EDUCATION variable takes the value of “High-educated” for cases when a respondent has “Four year college or university degree/Bachelor.s degree (e.g., BS, BA, AB)”, “Postgraduate or professional degree, including master's, doctorate, medical or law degree (e.g., MA, MS, PhD, MD, JD)”, or “Some postgraduate or professional schooling, no postgraduate degree” and “Low-educated” otherwise. In this task, we will test the difference of two proportions. Now, I am asking a bald question. “Are Republican-leaning Americans more educated than Democratic-leaning Americans?” Our parameter interest will be: The difference between the proportions of all Republican-leaning Americans and all Democratic-leaning Americans who are considered as highly-educated. p High − educated Rep − p High − educated Dem Our point estimate will be the difference between the proportions of sampled Republican-leaning Americans and sampled Democratic- leaning Americans who are considered as highly-educated. ^ p High − educated Rep − ^ p High − educated Dem a) Calculate the point estimate of our parameter of interest , p High − educated Rep − p High − educated Dem b) Assuming that the population parameter is normally distributed and all conditions for confidence interval calculations for proportion Team ___ [Enter your Team number in her] 1. Task 5: Statistical Inference Concerning Two populations

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10 Mini-Group Project 2 (8W section Fall’23), Team ____ differences met, calculate the appropriate standard error for the point estimate, ^ p High − educated Rep − ^ p High − educated Dem c) Construct a 90% confidence interval for proportion differences: d) Based on the 90% confidence interval values, what can you say about our research question? Do you have statistically significant evidence to say that the level of education differs across political leanings: proportion of Republican-leaning Americans who are considered as highly-educated differ from their democratic leaning counterpart? Please explain. Team ___ [Enter your Team number in her]