For Question 13, you will write a Final Report that summarizes and builds upon all your work from Questions 1 through 12. 13.Write a Final Report for this project. This is a cohesive report, not a series of responses to questions. Use the following guidelines to structure your report: 0 Introduction: Set the stage for your report by providing an overview of the categorical variable from your identied population. Include the identified population proportion and cite the source. (1-2 paragraphs) 0 Describe the process: How did you take your sample, what type of sampling did you use, and what bias(es) do you think might be present? Refer to Preview ZB for a discussion of sampling concepts and In-Class Activity 2B for a discussion of bias. (1-2 paragraphs) 0 Results: Summarize the results from your research and discuss how close your population proportion was to your sample proportion. Include any graphs andfor calculations that support your analysis. (24 paragraphs) 0 Conclusion: Provide an overview of the research you conducted. Include 2-3 good statistical questions related to your research you would like to investigate further. Include reflections about the project that would add insight. (1 paragraph) 1. Do a web search to find a proportion related to a categorical variable that interests you. The categorical variable must have only two categories, such as "yes" and "no." A. Write a sentence that identifies the proportion. (Example: 77% (p=0.77) of American women use Facebook, according to Pew Research. https://www.pewresearch.org/fact- tank/2021/06/01/facts-about-americans-and-facebook) 40%(p=0.4 of American adult use Instagram according to pew research https://www.pewresearch.org/fact-tank/2021/10/07/7-facts-about-americans-and-instagram/ B. Identify the population implied by your proportion. See Previews 2A and 9A for a few examples of identifying samples and populations. (Example: The population is all American women.) The population of American adults C. Write a sentence that identifies the categorical variable. (Example: The categorical variable is whether or not a woman uses Facebook.) The categorical variable is American adult's that do or don't use InstagramFor the rest of the project, we will assume that the proportion you identified in Question 1 is a population proportion. In Question 2, you will design your data collection process. Later in the project, you will compare your sample proportion to the assumed population proportion using Central Limit Theorem concepts. 2. Design your data collection process. A. What is your survey question? Be sure that it aligns with the categorical variable you identified in Question 1 Part C. (Example, "Do you use Facebook, yes or no?") Do you use Instagram yes or no B. How will you conduct your survey? (Example: I will use a combination of in-person interviews with female adult family and friends, and an Instagram poll. I will exclude any Instagram poll responses from males and children.) I will ask friends or family members do they use InstagramIn Question 3, you will record your survey results. 3. Take a sample of at least n=30 according to your approved plan from Question 2. In the table below, enter the individual responses from each of your survey respondents, typically \"yes\" or \"no.\" if your sample size is greater than 30, add rows in the table to record all results. In Questions 4 through 8, you will use the Central Limit Theorem for Proportions to predict usual values of sample proportions, assuming the population proportion you identified in Question 1 is accurate. 4. Using the identified population proportion from Question 1, and The Central Limit Theorem for Proportions, calculate the mean and the standard deviation for the sampling distribution of the sample proportion, forthe three sample sizes given below. If your sample size from Question 3 is not 30, 120, or 430, add a row to the table and perform the calculations for the sampling distribution of the sample proportion for your sample size. The symbol W stands for the mean of the sampling distribution of the sample proportion. The symbol o stands for the standard deviation of the sampling distribution of the sample proportion. Show your work. Sam le Size .. = p u p p(1 p) (Fig: 11 = 30 pg 2 0.4 0.400.51) 013 2 JT 2 0.894 n = 120 \"ii = 0.4 0.400.61) U T 0.045 n = 480 \"ii = 0.4 0.4(1D.61)_ U TD.0224 4. Using the identied population proportion from Question 1, and The Central Limit Theorem for Proportions, calculate the mean and the standard deviation for the sampling distribution of the sample proportion, for the three sample sizes given below. If your sample size from Question 3 is not 30, 120, or 480, add a row to the table and perform the calculations for the sampling distribution of the sample proportion for your sample size. The symbol |.I.'13 stands forthe mean of the sampling distribution of the sample proportion. The symbol U' stands forthe standard deviation of the sampling distribution of the sample proportion. Show your work. Sample Size n = 30 - _ r _ m = l$ = 0.394 n = 120 - . |_ - a = IMLLEM' = 0.045 n = 430 - . |_ - m |'4L:B:"'L'=.224 5. What do you notice happens to the standard deviation as the sample size increases from 30 to 120, and from 120 to 430'? (Hint: Does the standard deviation change in a pattern? It so: identify the pattern} THE NUMBERS DECREASES HALF AT EACH TIME 5. ln statistics, we often call values 'usual" when they are within 2 standard deviations of the mean. Using your sample size and the assumed population proportion: write a sentence that identies the usual values of the sample proportion. M22 941' =o.a1-2*o.ose= 0.432 mm M' =o.51+2*o.oso=o.rs: THE USALL'Y' VALUES ARE BETWEEN 0.432 AND ores 7". Using technology, and the identied population proportion, create the sampling distribution for each of the three sample sizes, and set the number of simulations to at least 1,000. Include a screen clip of each of these sampling distributions and the summary statistics. (Hint: Consider using the Sampling Distribution of the Sample Proportion App httgs:Hdcmathgathwayjsshinyagps.iotSangist prop!) Sampling Distribution of Sample Proportion Mean = 0.393, Sid Dev = 0.0879 (1,000 simulations of samples of size n = 30) 150 100 Frequency 50 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Sample Proportion p Sampling Distribution of Sample Proportion Mean = 0.401, Std Dev = 0.0448 (2,000 simulations of samples of size n = 120) 150 100 Frequency 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Sample Proportion p Sampling Distribution of Sample Proportion Mean = 0.4, Std Dev = 0.0219 (2,000 simulations of samples of size n = 480) 100- 75 Frequency 50 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Sample Proportion p8. In a paragraph (34 sentences), describe the shape, center, and spread of the three simulated sampling distributions of the sample proportion from Question 7. Do these align with what the Central Limit Theorem predicts? (Hint: You predicted the means and standard deviations in Question 4, and the Central Limit Theorem also predicts the shape of the distribution. See In-Class Activity 90 for more details.) The 3 graphs from question 7 have a Bell curve with a center with around the population proportion In Question 9 through 11 you will apply what you predicted in Questions 4 through 8 to the sample you recorded in Question 3. 9. Using technology, create a bar chart for your qualitative variable. Be sure to include descriptive labels in your bar chart. Include a screen clip of your bar chart here. (Hint: Consider using the Describing and Exploring Categorial Data App httgsvtdcmathgathways.shinyaggs.iotEDA categorical!) Bar Graph 1.5 1.3 Count 'f' ES r10 Instagram user 10.What is the sample proportion? Use appropriate notation and show the calculations. Include the numerical values for the success size, the sample size, and the decimal equivalent of the proportion. (Example, 35 = E m 0.7333 of sampled American women use Faeebook.) , p\" = g m 0.5667 of sampled gag, adult use lnstagram 11.Using 1-2 sentences, compare the sample proportion to your assumed population proportion. (Hint: Are they close to each other or far apart? Did your sample proportion surprise you? Is your sample proportion a \"usual\" value?) No the values are far apert but my sample proportion is % value 12. Identity and explain at least one type of bias that could be present in your sample collection procedure. (Hint: See ln-Class Activity 23 for a discussion of bias.) One type of bias is the age of the people who participate