Download Descriptive Statistics Homework

Descriptive Statistics Homework
A note about neatness. Your work must be neat and organized, otherwise I will require that you redo the
assignment on a word processor, including using the formula editor to show your work. This requirement
is to insure that you take pride in your work and also to help save Jim time when he grades your work.
Skim-read Chapters 1 through 3 in Howell. These are review chapters. You can likely answer
most of the questions below without reading the chapters prior.
1. Download the SPSS Distribution Data set from the course web site. Create histograms, stem-and-leaf
displays, and boxplots for the za, zb, zc, zd, ze, zf, and zg variables.
List the variables with distributions that are skewed right.
List the variables with distributions that are skewed left.
List the variables with distributions that are mesokurtic.
List the variables with distributions that are platykurtic.
List the variables with distributions that are symmetric.
List the variables with distributions that are uniform.
In which distribution are most of the scores on the high end of the scale?
In which distribution are most of the scores in the middle of the scale?
Carefully compare the histograms to the boxplots. Practice identifying the shapes of the distributions
from only the boxplots. Given these variables, what distribution shape do you think is most difficult
to identify from a boxplot?
Record the skewness and kurtosis statistics for each variable. Jim will show you how to get these
from SPSS. We did not cover them in lecture.
Run the tests of normality. Which variables significantly depart from normality? Again, we did not
cover these tests in class. Jim will show you how to request them from SPSS.
2. Using paper-and-pencil create an ungrouped Frequency Table and Frequency Histogram for the
following ages in years:
22, 22, 19, 21, 19, 22, 19, 19, 20, 20, 21, 21, 25, 19, 22, 24, 25, 23, 21, 20, 23, 23,
19, 19, 19, 19, 22, 20, 25, 25, 21, 20
Note that the lowest observed value is 19 and the highest observed value is 25. Use these values as
the low and high values in your table and graph.
What is the percentile rank of a person with an age of 23 in this sample?
Enter the data into SPSS and create a frequency table, a frequency histogram and a stem-&-leaf
display. Show Jim your SPSS output on the computer screen.
3. Consider a psychologist studying individuals' responses to different types of music. In one condition
of his study he asks ten participants to listen to loud alternative rock music (e.g., Tool) for five
minutes while he measures their heart rate in beats per minute with a photoplethysmograph. The
psychologist obtains the following average heart rates:
76.2, 82.1, 71.3, 77.9, 87.2, 81.7, 81.0, 72.1, 71.2, 77.9
What is the variable being measured?
What is the scale of measurement?
Compute the mean, median, mode, observed range, sum of squares (SS), estimated population
variance (s2), and estimated population standard deviation (s) for the data. Show all of your work.
What statistic(s) indicate the spread or variability of the data?
Based on one of the statistics you computed, how would you characterize the data in terms of
variability (Low / Medium / High). Briefly explain or justify your answer and be sure to indicate
which statistic you are relying on.
Enter the data into SPSS and check your answers for the mean, median, mode, variance, and standard
deviation. Turn in the SPSS printout.
z-scores
1. Suppose you complete a new questionnaire that measures your degree of Need for Cognition (that is,
your "desire" for cognitively challenging tasks). A high score on this questionnaire indicates high
need for cognition, and a low score indicates low need for cognition. You find that your z-score on
this questionnaire is -1.75. What does this z-score indicate, and is it extreme? Given only what is
written above, should you use Chebyshev’s rule or the Empirical rule to aid in your judgment of the
value?
2. Using SPSS, create a data set with six numbers such that their z-scores are all within the range of -1
to +1, but none of their z-scores is equal to 0. Hint: Look at the formula for the z-score and consider
what values it involves, then play around with different numbers until you come up with six that all
have z-scores between -1 and +1.
3. Using SPSS, create a data set of ten numbers such that one of the scores yields a z-score greater than
2.5. Hint: Again, you'll probably need to experiment with different numbers until hitting upon the
right combination.
4. Assume that the following z-scores came from a standard normal distribution. Report the proportion
of scores that fall below each of the z-scores. {sketch a diagram of the normal distribution, roughly
locate the z-value in the distribution, shade in the area you want, and then look the proportion up in
the z-table}
a. 0.45
b. -1.75
c. 0.00
5. Assume that the following z-scores came from a standard normal distribution. Report the proportion
of scores that fall above each of the z-scores.
a. 2.02
b. -2.55
c. 0.68
6. The following values, taken from a standard normal distribution, reflect the proportion of scores that
fall below a particular z-score. What z-score corresponds to each? {Here, you have to shade in the
area and then look up the z-value}
a.
b.
c.
d.
e.
0.95 (95%)
0.50
0.20
0.87
0.05
7. What proportion of scores from a standard normal distribution fall between the z-scores -0.44 and
1.10?
8. Suppose you wish to compare the mean performance of men and women on the quantitative portion
of the GRE. Your colleague (a fellow student) tells you that before comparing the two means you
need to convert the men’s scores to z-scores and then, separately, convert the women’s scores to zscores. You can then compare the means of the two sets of z-scores. He tells you to do this because
comparing men and women on the GRE is like comparing apples to oranges, and you can only do that
with z-scores. Is he giving you good advice? Why or why not?
9. In another study your professor tells you to examine your data for non-normality. If the data are not
normal, you need to use a type of normalizing transformation. You in fact find that your data are
radically skewed to the left. Your colleague tells you that you can easily transform your data to
normality by converting the data to z-scores. He reminds you that z-scores are normally distributed
and shows you the z-table in the back of his book. Is he giving you good advice? Why or why not?
10. Work problems 2.17, 2.18, 2.20, 2.22, 2.26, 2.32, 2.34, 2.36, 2.38 in Howell.
11. Work problems 3.2, 3.6, 3.8, 3.10, 3.14, 3.16, and 3.18 in Howell.