Distance Education Statistics
Lab C
Eric Parslow
and
Russell T. Hurlburt
University of Nevada, Las Vegas
This lab will consist of 4 parts:
Practice using the "Normal" program in ESTAT.
Practice converting raw data to z-scores and back to raw data.
Practice converting from raw data to area under a normal curve and back to raw data.
The quiz.
Note: a calculator may be helpful.
Part I - The "normal" program in ESTAT
1. Open ESTAT, open the program titled "Normal".
2. Take the tutorial to lean how to use the program.
3. Practice eyeball estimating the shaded area under the curves in each of the three 'Paths'.
4. In Path 1 and 2, your eyeball error should be consistently under 3%.
5. In Path 3, your eyeball error should be consistently under 9%.
Part II - Converting
X
to
z
and back again
1. In ESTAT, open "datagen".
2. Using the 'generate' function, generate random data in column 1.
3. 'Duplicate' the data in column 2.
4. Find the mean of column 1 in the results below (Xbar) and subtract that quantity from each value in column 2, using the 'edit variable' function (note that you can "add" a negative number to subtract).
5. 'Duplicate' column 2 in column 3.
6. Locate the value of the standard deviation of the data in column 1 (s). Note that it is the same for column 1 and 2.
7. Divide that value into each of the pieces of data in column 3, using the Edit Variable function. (Use your calculator to divide 1 by s and multiply each piece of data by that number.)
8. Column 3 is now a list of z scores, equivalent to the raw data in column 1.
9. Take note of a few characteristics of the z scores:
the sum of the column is 0.
roughly half of the values are positive and half are negative.
very rarely if ever, will any of the values be greater than
3.
10. As practice, convert by hand, the following values to either
z
or
X
, assuming that Xbar is 100 and
s
is 15.
a.
X
= 110
z
=_______________
b.
X
= 70
z
=_______________
c.
X
= 115
z
=_______________
d.
z
= 0
X
=_________________
e.
z
= 2.5
X
=________________
Answers:
a. .67
b. -2.00
c. 1.00
d. 100
e. 137.50
Part III - Computing the area under a normal curve.
1. Recognize that in the previous exercises, essentially, we were performing part of the conversion raw scores to percentiles.
2. The final step of the procedure is to look up the z score on the z score/area table in the back of the book (Table A.1)
3. In order to solidify your understanding of the use of this table and the process of conversion, answer the two following two questions (the correct answers will follow):
a. What percentage of IQ's (Xbar=100, s=15) are between 85 and 110.
b. What IQ score would you have to get to be in the top 5% of the population?
Answers:
a. 59%
Explanation:
(raw)85 = (z)-1 = (area to mean)34%
(raw)110 = (z).67 = (area to mean)25%
34% + 25% = 59% (total area under the curve)
b. 125
Explanation:
95% - 50% = 45%(area from mean to 5%)
45%(area) = 1.65(z)
1.65(z) * 15(s) = 24.75
100(mean) + 24.75(raw sore) = 124.75 (round to 125).
Part IV - The Quiz.
If your answers were incorrect, review the explanations and attempt the problems again. For additional practice, change some of the numbers in the questions and solve.
Once you have mastered all of the skills in Parts 1-3, you are ready to take the quiz.
You will need the quiz password, which is
7654321
