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Test Topics Notation and symbols Determining if CLT applies.

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## Test Topics Notation and symbols Determining if CLT applies.

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**Test Topics**Notation and symbols Determining if CLT applies. Using CLT to find mean/mean proportion and standard error of sampling distribution Finding confidence intervals (means & proportions) Finding sample size to get specific margin of error**CI = statistics ± z* · standard error**margin of error What if you want the margin of error to have a certain value because you want to estimate the TRUE mean or proportion within a specific amount? Example:You want to estimate your candidates approval rating (%) within 3% of the ACTUAL approval rating across the country.**Often a high confidence level (95 or 99%), means that your**interval must be very large (high margin of error). Ultimately, we would like to create a confidence interval with a high confidence level and very small margin of error. How can we control that??? Make the z* value smallerthis means a lower confidence level. Make the s value smaller this does make it easier to get a more accurate m, but is difficult to control. Make the n (sample size) larger dividing by a larger number makes the standard error smaller and in turn the margin of error smaller. Best Option!**The one part that would have the power to change the margin**of error is the sample size (n). Margin of error • z* will be determined by the confidence level • or will be determined by the data • Given a certain margin of error (E), • we can solve for n.**Example: We want to estimate the average number of college**games attended by all football fans per season within 2 games based upon a 95% confidence level. We know that s = 3.5 games. E Multiply by Divide by 2 Square both sides**Example: We want to estimate the average number of college**games attended by all football fans per season within 2 games based upon a 95% confidence level. We know that s = 3.5 games. *We could solve the formula for “n” and use it each time we need to compute a sample size. E Multiply by Divide by E Square both sides n**Example:You want to estimate your candidate’s approval**rating (%) within 3% of the ACTUAL approval rating across the country. You want to be 99% confident that your estimate is accurate and know that = 0.43. What is the minimum sample size needed to make this happen? This is a proportion. Divide by 2.575 Square both sides Multiply by n and then divide***We could solve the formula for “n” and use it each time**we need to compute a sample size. Divide by z* Square both sides Multiply by n Then divide OR )