In this week’s reading, the text discusses different types of samples and their distributions, sampling errors, probabilities, and confidence intervals. Using Excel, complete the following problem. this task involves calculating the required sample size to estimate a population proportion with 90% confidence and a ±5% margin of error. it requires an Excel-based statistical modeling, please apply the correct formula and Excel tools to clearly compute the required sample size. also provide all equations used on an organized spreadsheet, and a concise explanation of the methodology.
Problem: You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Coke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 90% confidence, the proportion of people preferring Coke to within 5% of the actual value? Show all of your work. In your Excel spreadsheet, Identify the sample size. Utilize Excel support tools. Present any equations utilized. Assume that roughly half the population prefers Coke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 90% confidence, the proportion of people preferring Coke within 5% of the actual value? This problem has to do with the selection of sample sizes for proportions as discussed in section 8-9b. To do this we need to use formula 8.19: n = [ (z-multiple) / B ]^2 (p_est)(1 – p_est) [Note: symbol ^ means ‘to the power of’] The values for half-length, B, and p_est are all given in the statement of the problem. The next step is to find the z-multiple. As explained in section 8-5, a z-multiple is a cut-off value in the normal probability distribution for a given probability. For your convenience, I have listed below values for z-multiple corresponding to different confidence levels: Confidence Level / z-multiple 95% 1.96, 90% 1.645, 98% 2.33, 99% 2.58, This problem is pretty much like example 8.10 in section 8-9b, hence you can use the same strategy to arrive at the solution. Figure 8-17 even shows the Excel functions used for various calculations. To find the z-multiple, you could either use the above table or compute it directly using Excel’s NORM.S.INV function as in example 8.10. Here is a video tutorial that you might find helpful: https://youtu.be/_QEddJG2MN0?t=200Links to an external site. https://www.youtube.com/watch?v=o9jQaYwZ5cE&feature=youtu.be https://www.youtube.com/watch?v=laCIJa7m4ao&feature=youtu.be
