Transcript 2.2.2 - GEOCITIES.ws

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