To: sbaker@odu.edu
From: Thomas Meyer
tmeyer@ph.vccs.edu
276 656-0283
Patrick Henry Community College
Subject: Statistics - w/ Dr.Spencer Baker - Homework Assignment #1, Ch 4 - Problem 08, page111.
Date: February 9, 2004
Question:
For the box plots on page 111, compare the different distributions
in terms of their location and spread.
a.
According to gender role socialization theories, females should score higher
than males on empathic concern. What can you conclude from the index of
location and spread of the date? Justify your answer.
Answer:
Box and whisker plots are explained in the text on page 92.
From the pictures on page 111, we can see that for females and males:
Regarding Location:
On the horizontal or X-Axis we discovered that:
N=60 for both females and males.
Regarding Spread:
Measures of empathic concern were recorded on the Y-Axis. We discover
that:
(1) medians of the respective distributions
are essentially equal at approximately 32;
(2) interquartile ranges for females are not more than a point or two
points higher than those for men;
slightly more women are in the 3rd quartile and slightly fewer women are in the
2nd quartile;
for men quartiles 3 and 2 contain approximately equal numbers of men.
(3) the range for both females and for men are essentially equal with the
top scores on empathic concern of approximately 49 and lowest scores of about 20
for females and 19 for men.
Conclusion:
Females do NOT score that much higher than
men on this measurement of empathic concern. Men and women are more equal
in terms of empathic concern than the theory would suggest. Here are some
possible reasons why:
(1) Perhaps the theory is wrong.
(2) Perhaps other men and women could be tested.
(3) Perhaps some other method of measuring empathic concern would bring a
different result.
(4) Perhaps the samples were not randomly
chosen.
Question:
b. Forty rats were trained to run a maze for five weeks. The rats did not differ in running speed and were randomly assigned to four groups.
Answer:
Description:
10 rats constitute a control group and received no
treatment. Their box and whisker plot shows a median maze completion time
of about 85 seconds. Their range was from about 70 to 90 seconds.
The interquartile range was rather narrow, from 80 to about 89 seconds.
10 rats with 2% aluminum sulfate in their water constitute the second group and
take longer to run the maze. Their box and whisker plot shows a median
maze completion time of about 125 seconds. Their range was from about 110
to 130 seconds. The interquartile range was wider, from 115 to about 128
seconds.
10 rats with 4% aluminum sulfate in their water constitute the third group and take still longer to run the maze. Their box and whisker plot shows a median maze completion time of about 130 seconds. Their range was from about 128 to 150 seconds. The interquartile range was from 130 to about 145 seconds.
10 rats with 8% aluminum sulfate in their water constitute the fourth group and take the longest period of time to run the maze. Their box and whisker plot shows a median maze completion time of about 146 seconds. Their range was from about 140 to 165 seconds. The interquartile range was from 145 to about 155 seconds.
Conclusion:
Their appears to be a direct, though nonlinear relationship between the amount
of aluminum sulfate added to drinking water and time needed to complete the
running of the maze. Deterioration in running the maze is most pronounce
with the onset of the 2% solution. Doubling the solution and then doubling
the solution again seems to create a linear increase in the time required to run
the maze.
This could be an interesting finding if it generalizes to human beings. It suggests that diseases like Alzheimer's might have as an explanation that concentrations of aluminum in water can cause deterioration in mental functions.
filename: StatHW1Ch4Prob08page111TomMeyer.doc
Tom Meyer
Thomas Meyer