Assessing Normality Section 2.2.2

Starter 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 L FLIPS 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 x min = μ - 3σ, x max =μ + 3σ, x scl = 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 percentages.

Assess Normality with a Normal Probability Plot (Ex 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 L 1 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 L 1. 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