Exercise 1.104.

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Normal probability plots.

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It
is quite easy to make a normal probability plot with Excel. In this
exercise we generate

100
observation from the standard normal distribution and make a normal probability
plot

of
the data.

To start we generate those 100 observations from N(0,1):

Open the
Random Number Generator window from the Data Analysis toolbox and fill
the options as to

generate 100 observation from N(0, 1)
in the cells A1:A100.

Sort the data in ascending order.

Next you will create in the column B a
sequence of 100 z-scores such that in-between each two of them the area

under the Standard Normal Distribution
curve to be equal with 1/100 i.e. 1/(the number of observations).
It is

quite easy to create such a sequence for
N = 100, but you will do it in such a way that you may use the worksheet

for any other data set with with any number
of observations

First,

Put the number 0.5 in the cell **D1** and put 1.5 in the
cell
**D2.**

Highlight** both** cells. Then
the screen should look something like:

Turn this into a long column of counting numbers, 0.5, 1.5, 2.5,...,99.5,
by using the mouse

to pull the little square (on the lower
right hand corner of the highlighted box) downwards to the entry **D100.**

Be sure that you highlight** both**
cells before dragging down, otherwise you will get only 1.5s!

Now,

Highlight the cell **C1, **then type the following formula:

Drag the right little square of the cell
**C1
down** to the **C100. **You got the grid of percentile values.

Next we compute in the column B the z-scores
of the values from column C.

In
the cell B1 type:

Drag the right little square of the cell
**B1**
down to **B100. **The first rows should look like
in the image above.

You may check that you got the right sequence
of z-scores by plugging in the worksheet from Ex.1.82 the values

from the cells B1:B2 (or any other two
adjacent cells from the column B) and observing the resulting output:

**Note.** The numbers
from column A are different for every random sample.
But it may happen that you'll get exactly

the same sample as in the image if you
just started Excel.

Now you will make the normal probability
plot.

Highlight the cells **A1:B100. ** Choose **Chart**, then
**XY(Scatter)
and** the first sub-type. Click "**Next**"

and choose the "**Series**" option
and choose the column **B **for the **X-axis** and column **A**
for **Y-axis**. (You want

to have the z-score on the X-axis.
Click "**Next**" to get to the "**step 3 of 4**" and chose to have
grid lines for both axis:

Click
**"Finish"**.
The the normal probability plot will appear. Clear (delete) the legend
and format the

axis as below.

Be sure that your chart is square shaped
for the best display of the plot.

As you observe the this normal quantile
plot lie almost on the diagonal as you expected to be because your data

from the column A is sampled from the
Standard Normal Distribution.

Reload data in the column A ten times with
the Random Number Generator . Each time you will
get a similar diagonal plot!

**Question.
Hand in an Excel worksheet with a normal quantile plot for the guinea
pig survival time**
**from
table 1.5. in a format similar to the above image.**
**Note.
The Y-axis should have the range [0, 600] as in Fig 1.38 from the textbook.**

**Explain
briefly how this data set deviate from normality.**