Assessing Normality Section 2 2 2 Starter 2

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 FLIP 50 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 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 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