Q Evaluate Computing and interpreting confidence intervals are an important part of statistical inference. For this discussion, you will get to make your own confidence intervals. Do one of the following two options: Recall, from Module 1, numerical data is said to be quantitative. Examples of quantitative data are the weight of an adult, the number of home runs, the price of a new car, and the speed of a runner. Data that is a category and not necessarily numerical is said to be qualitative. Examples of qualitative data are hair color, human blood type, gender, nationality, and hurricane category. (1) Collect 50 or more qualitative data items. Use the same method of collecting 50 or more data items that you used in the Module 1 discussion. Then, construct a 90% confidence interval for the population proportion, p. View an example on how to use StatCrunch (with data) to compute confidence intervals for a population proportion. Then, answer the following: • o Briefly describe your data set o Include your Statcrunch report, either as an attachment or (even better) paste is into your discussion post o Write down your sample size. o From your data, what is the point estimate, p? of the population proportion? o Write down the confidence interval that you obtained. Interpret the result. o What is the margin of error? o Using the same data, construct a 98% confidence interval for the population proportion. Then, answer the following three questions: (i) What happens to the length of the interval as the confidence level is increased? (ii) How has the margin of error changed? (iii) If the sample size is increased, what do you think will happen to the margin of error? Why? OR (2) Collect 50 or more quantitative data items. Use the same method of collecting 50 or more data items that you used in the Module 1 discussion. You may even use the same data that you used in Modules 1 or 2. Then, construct a 90% confidence interval for the population mean, ?. View an example on how to use StatCrunch (with data) to compute confidence intervals for the population mean. Then, answer the following: • o Briefly describe your data set o Include your Statcrunch report, either as an attachment or (even better) paste is into your discussion post o Write down your sample size o From your data, what is the point estimate, x?, of the population mean? What is the sample standard deviation? o Write down the confidence interval that you obtained. Interpret the result. o What is the margin of error? o Using the same data, construct a 98% confidence interval for the population mean. Then, answer the following three questions: (i) What happens to the length of the interval as the confidence level is increased? (ii) How has the margin of error changed? (iii) If the sample size is increased, what do you think will happen to the margin of error? Why? Assume that the confidence interval methods mentioned in the textbook apply to your data. Make sure your data set is large enough (50 items or more). Please be sure to follow your primary posting with at least two substantive reply posts to your peers. In your response to classmates, you may discuss one of the following: a. Ask your classmate a question about his/her result that is not clear to you. b. Share something that you see about your classmate’s results that your classmate did not mention. You may also discuss specific details about the type of data. For example, if the confidence intervals are about weights of adults, then you may discuss unique details related to this type of data. c. Share what you have learned from your classmate’s results. ________________________________________ Your initial post is due by Thursday at 11:59 PM ET. Your responses are due by Sunday at 11:59 PM ET. Consult the Discussion Posting Guide for information about writing your discussion posts. It is recommended that you write your post in a document first. Check your work and correct any spelling or grammatical errors. When you are ready to make your initial post, click on "Reply." Then copy/paste the text into the message field, and click “Post Reply.” This is a “post first” discussion forum. You must submit your initial post before you can view other students’ posts. To respond to a peer, click “Reply” beneath her or his post and continue as with an initial post. ________________________________________ Evaluation This discussion will be graded using the discussion board rubric. Please review this rubric, located on the Rubrics page within the Course Introduction module of the course, prior to beginning your work to ensure your participation meets the criteria in place for this discussion. All discussions combined are worth 20% of your final course grade.