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Assessing Normality Section 2.2.2 Starter 2.2.2 • For the N(0, 1) distribution, use Table A to find the percent of observations between z = 0.85 and z = 2.3 Today’s Objectives • Determine whether a distribution is approximately normal by three different tests: – Assess symmetry and shape – Assess the empirical rule – Use a Normal Probability Plot Assess Normality by Shape • Consider the data you stored from the FLIP50 program in a list called FLIPS • Run 1-Var Stats LFLIPS • Write down the mean and s.d.; We will use them shortly – For symmetric data, μ=M; Does it here? – Is a boxplot reasonably symmetric? – Is a histogram reasonably mound-shaped? • So far, the data look normal – Now let’s check the Empirical Rule Assess Normality by Empirical Rule • The histogram would be useful for counting observations within each border group if only it had the borders we want. • You can set up the borders by setting xmin = μ - 3σ, xmax=μ + 3σ, xscl = σ – This will give you exactly 6 bars, each exactly one standard deviation wide. • Do so now, using the mean and s.d. you noted previously from 1-Var Stats • Count the observations and calculate the percents in each bar; compare with the 68-9599.7 percentages. Assess Normality with a Normal Probability Plot (Ex. 2.10 p 94) Set up Plot 1 as a Normal Probability Plot – It’s the last of the 6 available icons under “Type” • Set Data List to be FLIPS • Tap Zoom 9 to see the plot • If it is approximately a straight line, that is good evidence that the data are approximately normal. – The graph is plotting z-score against x (the raw score) – Normal data will form a straight line pattern Testing Uniform Data for Normality • Clear L1 and enter rand(100) at the top – You should get a new list of 100 numbers • Look at 1-Var Stats – Mean = median because uniform data are symmetric (but not normal) • Look at a histogram using a window of [0,1] .1 – Notice that there is NOT a mound shape • Look at the Normal Probability Plot – The plot is not linear because the data are not normal Class Activity • Roll two dice 36 times. Record the sums in L1. • Are the data approximately normal? Apply all three tests to decide. – Mound-shaped with mean = median? – Empirical Rule met? – Normal Probability Plot roughly linear? • Write a sentence or two that states your conclusion Today’s Objectives • Determine whether a distribution is approximately normal by three different tests: – Assess symmetry of shape – Assess the empirical rule – Use a Normal Probability Plot Homework • Read pages 92 – 96 • Do problems 26 – 30