Fanr 3000 1st Edition Lecture 10Outline of Last Lecture I. Hypothesis Testing II. T-TestsIII. Types of T-tests Outline of Current Lecture I. Determining Sample SizeII. Calculate Sample SizeCurrent LectureI. Determining Sample Size- Mean+/- variance o Increase samples= decrease variance - Subject to time, budget, and ease of selection constraints o Task: determine how large of a sample a “good” estimate of population parameter would require - Determine how much error you are willing to accept in estimating the mean of a populationo Sample size should be statistically and practically efficient II. Calculate Sample Size 1. Using the bound on the sampling meana. Based on the absolute amount of error acceptable based on the standard error of the mean b. Bx= 2Sx 2. Using the standard deviation and desired closeness, or coefficient of variation (%,CV) and allowable/acceptable error (%, AE) - The formula used varies based on whether or not N (# in population) is known- Finite population= when N is knowno Using BOUND on the sampling meanThese 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.n = number of individuals you will need to sampleN = number of individuals in your populationB = your “bound” – typically 2 times your Standard Error (but doesn’t have to be)s² = your variance As the bound decreases (less error willing to accept), you have to sample more 1. We need N (total # of observations in the population)2. We need to determine a desired bound on the population mean 3. We need to estimate the variance expected in the population a. Pilot sampleb. Information from other similar population o Using CV & AEWhen we want to achieve a certain allowable error (%) we can use a similar equation:Where CV = the coefficient of variationAE = allowable error (%) As the allowable error decreases (less error willing to accept), you have to sample more 1. We need N (total # of observations in the population)2. We need to determine a desired allowable error (%) on the population mean 3. We need to estimate the CV expected in the population - Infinite population= when N is unknown o Need to know: The standard deviation or the CV The desired objective (e.g., to be within 3 ounces of the true weight of a bird) or the allowable error (e.g., 5% error) or - Where : t= tn-1,α/2 and E= desired objective o ALWAYS ROUND UP!!!o Practical considerations1. Cost2. Trading off allowing error and/or confidence is an acceptable