FANR 3000 1st Edition Lecture 7 Outline of Last Lecture I Normal Distribution II Z Distribution III Percentile Outline of Current Lecture I Data Interpretation and T table II Confidence intervals Current Lecture I Data Interpretation and T table a T distribution i More area in the tails and less in the center than z distribution ii As n increases though a t distribution will approach the standard normal distribution iii T values allows us to estimate uncertainty Alpha acceptable probability of error o As we want to be more confident in our analyses we decrease our alpha level o Alpha value is the acceptable probability of confidence the inferences you make from the data you collect is wrong Decrease in alpha levels more confidence levels Acceptable probability of error is the alpha value Ex For 95 confidence we are saying that we are willing to accept a 5 chance our range of possible means is wrong so alpha 05 Based on your degrees of freedom you can calculate t score from any alpha level interested o df degrees of freedom n 1 within the distribution there is a true population mean more samples results in less variability tighten cluster of t distribution less range of predicted values more confident more accurate numbers These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute II less samples more variability bad Confidence intervals A way to incorporate our sampling error in our population parameter estimate Range of values around a sample mean that has a probability of containing the true population mean Steps for determining confidence interval 1 Calculate mean of sample 2 Calculate variance SD and SE 3 Determine critical value from distribution table 4 Plug values into CI formula As CI increases the CI get wider Decrease variability add more samples Smaller sample sizes generate wider intervals