Download Stat 401 Lecture note

Stat 401 Lab Activity 3
Part I. The Normal distribution.
Read about the normal distribution from ch05t.pdf of the lecture notes (from page 12
until Proposition 3.4 on page 21).
1. Plotting the Normal Probability Density Function.
We will plot normal pdfs through Minitab. These set of commands can be used for
plotting the pdf of other random variables as well.
a) Generate data from -3.4 to 3.4 in steps of 0.01:
Calc>Make Patterned Data>Simple Set of Numbers> Store Patterned Data in “C1”;
From first value “-3.4”; To last value “3.4”; In step of “0.01”, OK.
b) Find the value of the probability density function of N(0,1) for each entry in C1:
Calc> Probability Distributions > Normal> check “Probability Density”; enter “0”
and “1” for Mean and Standard Deviation; enter “C1” and “C2” for Input column
and Optional storage, OK.
c) Do a scatter plot (with Connect Line) of C1 as X and C2 as Y.
Next we will superimpose the plot of the pdf of N(0,1/16) to that of the pdf of N(0,1).
Note that N(0,1/16) is the pdf of the sample mean of a sample of size n=16 from a N(0,1)
population.
d) Repeat step b), but change “1” to “0.25” for Standard Deviation, and enter “C3” for
Optional storage.
e) Graph> ScatterPlot > With Connected Line> input “C2” and “C1” under Y and
X in the first row, and input “C3” and “C1” under Y and X in the second row; Click
Multiple Graphs, select “Overlaid on the same graph”, OK, OK.
2. Finding Normal Probabilities and Population Percentiles
To find a percentile, such as the 95th of a normal distribution, first enter “0.95” in a
column, e.g. column c4, and follow the commands
Calc> Probability Distributions> Normal> Select “Inverse cumulative probability”;
fill “0 and 1” for Mean and Standard Deviation; select “C4” and “C5” for Input
column and Optional Storage, OK.
Several percentiles can be found at once, by entering, e.g.0.25, 0.5, 0.75, 0.950 in C4 and
using the above sequence of commands.
To find the cumulative distribution use the above sequence of commands except for
selecting “Cumulative probability” instead of “Inverse cumulative probability”..
Part II. The Normal Probability Plot.
Probability plots plot sample percentiles vs population percentiles. They are used to
ascertain the extend to which observed data conform to an assumption about the
population distribution. A straight line at 45 degrees validates the distributional
assumption. The normal probability plot is used to check the conformance of the data to
the assumption that the population distribution is normal.
Calc > Random data > Normal > Enter 59 in “Generate BLANK rows of data”,
enter c10 in “Store in column(s)”, enter mean and standard deviation > OK
Now we will do the normal probability plot to confirm the normality assumption:
Graph> Probability Plots> Select “Single”> Enter C10 for Graph variable; click
Distribution> select “Normal” under distribution; 0 and 1 for Mean and StDev. OK,
OK.
Part III. To be turned in together with your hw on Wednesday.
a) Overlay the plots of the cdf for N(0,1), and N(0,1/16). Turn in the plot.
b) Generate 50 random data from the normal distribution with mean 1 and standard
deviation 0.25. Do the probability plot to confirm normality assumption, but use
mean 0 and standard deviation 1, i.e. use the exact probability plot commands we
gave in Part II. Does the plot appear linear?
c) Generate 50 random data from the Gamma distribution with shape parameter 2
and scale parameter 1. Do the normal probability plot leaving the mean and
standard deviation unspecified. Does the plot appear linear?