Test Topics 1)Notation and symbols 2)Determining if CLT applies. 3)Using CLT to find mean/mean proportion and standard error of sampling distribution 4)Finding confidence intervals (means & proportions) 5)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 smaller this means a lower confidence level. Make the  value smaller this does make it easier to get a more accurate , 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).

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  = 3.5 games. 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  = 3.5 games. Divide by E Square both sides *We could solve the formula for “n” and use it each time we need to compute a sample size.

Divide by Square both sides Multiply by n and then divide

Divide by z* Square both sides Multiply by n *We could solve the formula for “n” and use it each time we need to compute a sample size. Then divide