Overview For this paper, you will investigate biased questions. After you create your own neutral and  biased questions, you will gather data to examine if the wording you used had an effect on how  people answer. Here are examples of two different biased questions. 1 • According to research from The Journal of the American Medical Association, “stronger  gun policies were associated with decreased rates of firearm homicide, even after  adjusting for demographic and sociologic factors.” 2 Do you support or oppose stricter  gun control laws in the United States? • The United States Constitution says, “the right of the people to keep and bear Arms, shall  not be infringed.” Do you support or oppose stricter gun control laws in the United  States? Both questions ask about the person’s ideas about gun control, but they position them differently. (People are likely to have strong opinions on gun control already; I suggest you  choose a less contentious topic.) A more neutral version would be “do you support or oppose stricter gun control laws in the  United States?” (Note that this is still a little bit biased. There is a small bias because of the word  order – support is first – so in a real-world situation it would be best to change the order  randomly when you asked people, putting support first half the time and oppose first half the  time. Using the word “stricter” will also potentially influence people’s responses. It’s nearly  impossible to write a perfectly neutral question; you’re just going to do the best you can.)   1 Other examples can be found at: https://www.qualtrics.com/blog/writing-survey-questions/ and  http://danielsroar.weebly.com/uploads/5/3/1/4/5314494/pg_46_biased_or_unbiased_practice_answers.pdf 2 From Firearm Laws and Firearm Homicides: A Systematic Review | Firearms | JAMA Internal Medicine | JAMA  Network Information downloaded 6/12/202 (Found via On gun violence, the United States is an outlier | Institute for Health Metrics and Evaluation)  Math 125, Paper One Spring 2023 (5% of Final Grade) Your paper should include: A discussion of the questions  Pick a topic that interests you and come up with a neutral yes/no question about it. (If you’d  prefer your question could be support/oppose or another binary choice.) Give the neutral version and explain why you picked it. You should also explain why you think it is  neutral. (Please pick a question where you think the probability of a “yes” is between 25% and  75%. It’s okay if you turn out to be wrong, but you should aim for that – our statistical methods  work best if the probabilities aren’t close to 0% or 100%.)  Rephrase the question to be biased toward a “yes” or “no” response. (It does not need to be the  case that more than half the people choose that answer; it just needs to be that you think they  would be more likely to choose it than they were before.) Make sure your question is still about the same basic situation. Discuss: 1) how you developed the biased questions,  2) why you think the question is biased, and  3) what answer it is supposed to be biased towards. You will get feedback from me and your fellow classmates in the second discussion forum. A discussion about populations & sampling  Note: Even if you are not going to actually ask people the questions (another option is  given below), pretend that you are for this section. Discuss what population you’d like to  get information from, what type of sampling you’d use, and how you would create such  samples. Describe the population that you are interested in asking these questions to and why you chose  it. Be sure to use the same population for both questions. This population could be an online one (for instance, you can use social media). Or it could be a population you interact with at work,  etc. Math 125, Paper One Spring 2023 (5% of Final Grade) Create two separate samples, with 35 people in each. You should be sampling the same  population both times.  Identify the type of sampling technique you selected and explain why you chose it. You should  also discuss whether your sampling technique is likely to give you useful data. Are there any  potential problems with your technique? Data collection  • Option One (preferred and also more interesting): gather some real-world data.  Ask the people your questions. Thirty-five people should answer your neutral question (this is  your first set of data); thirty-five people should answer the biased question (this is your  second set of data). These should be different people. Record your raw data and include the  raw data in the paper.  • Option Two: work with computer-generated data. In this case, since you’ll have less work  with data gathering, I want you to analyze three sets of data.  Go to https://www.random.org/sequences/ and generate a sequence with smallest value 1  and largest value 50. Look at the first thirty-five responses. Assume all even numbers are  “yes” responses and all odd numbers are “no” responses. Record these responses as your  first set of data and include them in the paper.  Then go to https://www.random.org/integers/ and generate of sequence of thirty-five  numbers where each integer has a value between 1 and 150. Assume all multiples of three are “yes” responses and all other numbers are “no” responses. Record these responses as  your second set of data and include them in the paper.  Go to https://www.random.org/integers/ Generate a different sequence of thirty-five  numbers where each integer has a value between 1 and 150. Assume all even numbers are  “yes” responses and all odd numbers are “no” responses. Record these responses as your  third set of data and include them in the paper.  Math 125, Paper One Spring 2023 (5% of Final Grade) Presentation of Data  Calculate the percentage of “yes” and “no” responses for each set of data. Give your results in a  relative frequency distribution table. Pick at least one appropriate way to represent the data sets visually. You can represent each  data set with its own image or combine them into one image, depending on the type of visual  you select. Please do not use a frequency distribution here – you already did that – but any other  appropriate method is fine. I would suggest using Excel to create your images, since you can cut and paste them into a Word  document. However, you can use other software, if you’d prefer. I’ve used Desmos and  WolframAlpha to create some of the examples in the slides; there are links to other options on  Brightspace. You could also draw one by hand and insert an image of it. Extra Credit: Include additional appropriate visual representations of your data.  Conclusion  • If you chose Option One: Do you think that the different wording influenced the results?  Explain, based on your data. Either answer could be fine, as long as you explain why your  data support that.  • If you chose Option Two: Do you think that “yes” responses were equally likely in all three  sets of data? Do you think they were equally likely in any pairs of data sets? Explain your  reasoning. There is not necessarily a correct answer, as long as you explain why your data  support your reasoning. You won’t be able to talk about the wording of your questions, since  you didn’t actually gather data based on those questions. Throughout the paper, you try to show mathematical understanding of the situation.  

 Overview For this paper, you will investigate biased questions. After you create your own neutral and  biased questions, you will gather data to examine if the wording you used had an effect on how  people answer. Here are examples of two different biased questions. 1 • According to research from The Journal of the American Medical Association, “stronger  gun policies were associated with decreased rates of firearm homicide, even after  adjusting for demographic and sociologic factors.” 2 Do you support or oppose stricter  gun control laws in the United States? • The United States Constitution says, “the right of the people to keep and bear Arms, shall  not be infringed.” Do you support or oppose stricter gun control laws in the United  States? Both questions ask about the person’s ideas about gun control, but they position them differently. (People are likely to have strong opinions on gun control already; I suggest you  choose a less contentious topic.) A more neutral version would be “do you support or oppose stricter gun control laws in the  United States?” (Note that this is still a little bit biased. There is a small bias because of the word  order – support is first – so in a real-world situation it would be best to change the order  randomly when you asked people, putting support first half the time and oppose first half the  time. Using the word “stricter” will also potentially influence people’s responses. It’s nearly  impossible to write a perfectly neutral question; you’re just going to do the best you can.)   1 Other examples can be found at: https://www.qualtrics.com/blog/writing-survey-questions/ and  http://danielsroar.weebly.com/uploads/5/3/1/4/5314494/pg_46_biased_or_unbiased_practice_answers.pdf 2 From Firearm Laws and Firearm Homicides: A Systematic Review | Firearms | JAMA Internal Medicine | JAMA  Network Information downloaded 6/12/202 (Found via On gun violence, the United States is an outlier | Institute for Health Metrics and Evaluation)  Math 125, Paper One Spring 2023 (5% of Final Grade) Your paper should include: A discussion of the questions  Pick a topic that interests you and come up with a neutral yes/no question about it. (If you’d  prefer your question could be support/oppose or another binary choice.) Give the neutral version and explain why you picked it. You should also explain why you think it is  neutral. (Please pick a question where you think the probability of a “yes” is between 25% and  75%. It’s okay if you turn out to be wrong, but you should aim for that – our statistical methods  work best if the probabilities aren’t close to 0% or 100%.)  Rephrase the question to be biased toward a “yes” or “no” response. (It does not need to be the  case that more than half the people choose that answer; it just needs to be that you think they  would be more likely to choose it than they were before.) Make sure your question is still about the same basic situation. Discuss: 1) how you developed the biased questions,  2) why you think the question is biased, and  3) what answer it is supposed to be biased towards. You will get feedback from me and your fellow classmates in the second discussion forum. A discussion about populations & sampling  Note: Even if you are not going to actually ask people the questions (another option is  given below), pretend that you are for this section. Discuss what population you’d like to  get information from, what type of sampling you’d use, and how you would create such  samples. Describe the population that you are interested in asking these questions to and why you chose  it. Be sure to use the same population for both questions. This population could be an online one (for instance, you can use social media). Or it could be a population you interact with at work,  etc. Math 125, Paper One Spring 2023 (5% of Final Grade) Create two separate samples, with 35 people in each. You should be sampling the same  population both times.  Identify the type of sampling technique you selected and explain why you chose it. You should  also discuss whether your sampling technique is likely to give you useful data. Are there any  potential problems with your technique? Data collection  • Option One (preferred and also more interesting): gather some real-world data.  Ask the people your questions. Thirty-five people should answer your neutral question (this is  your first set of data); thirty-five people should answer the biased question (this is your  second set of data). These should be different people. Record your raw data and include the  raw data in the paper.  • Option Two: work with computer-generated data. In this case, since you’ll have less work  with data gathering, I want you to analyze three sets of data.  Go to https://www.random.org/sequences/ and generate a sequence with smallest value 1  and largest value 50. Look at the first thirty-five responses. Assume all even numbers are  “yes” responses and all odd numbers are “no” responses. Record these responses as your  first set of data and include them in the paper.  Then go to https://www.random.org/integers/ and generate of sequence of thirty-five  numbers where each integer has a value between 1 and 150. Assume all multiples of three are “yes” responses and all other numbers are “no” responses. Record these responses as  your second set of data and include them in the paper.  Go to https://www.random.org/integers/ Generate a different sequence of thirty-five  numbers where each integer has a value between 1 and 150. Assume all even numbers are  “yes” responses and all odd numbers are “no” responses. Record these responses as your  third set of data and include them in the paper.  Math 125, Paper One Spring 2023 (5% of Final Grade) Presentation of Data  Calculate the percentage of “yes” and “no” responses for each set of data. Give your results in a  relative frequency distribution table. Pick at least one appropriate way to represent the data sets visually. You can represent each  data set with its own image or combine them into one image, depending on the type of visual  you select. Please do not use a frequency distribution here – you already did that – but any other  appropriate method is fine. I would suggest using Excel to create your images, since you can cut and paste them into a Word  document. However, you can use other software, if you’d prefer. I’ve used Desmos and  WolframAlpha to create some of the examples in the slides; there are links to other options on  Brightspace. You could also draw one by hand and insert an image of it. Extra Credit: Include additional appropriate visual representations of your data.  Conclusion  • If you chose Option One: Do you think that the different wording influenced the results?  Explain, based on your data. Either answer could be fine, as long as you explain why your  data support that.  • If you chose Option Two: Do you think that “yes” responses were equally likely in all three  sets of data? Do you think they were equally likely in any pairs of data sets? Explain your  reasoning. There is not necessarily a correct answer, as long as you explain why your data  support your reasoning. You won’t be able to talk about the wording of your questions, since  you didn’t actually gather data based on those questions. Throughout the paper, you try to show mathematical understanding of the situation.