Practical exercises
1 A recent study of 15 families focusing on the number of children per family found that seven families had one child, four had two children, two had three and another two families had four or more children. These figures are summarised in the following table:
| Number of families Number of children | |||
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| 7 | 1 | ||
| 4 | 2 | ||
| 2 | 3 | ||
| 2 | 4 or more | ||
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| Your task is to present the data in the form of a bar chart and a pie
graph. |
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2
A lecturer was interested in finding out how much
money students spend each week on entertainment, and asked 15 students to state
how much they spent on entertainment the week prior to the survey. The responses
were grouped in four spending groups, ranging from those spending less than
$20.00 per week, through to those spending $21.00-$40.00, $41.00-$60.00, and
more than $60.00. The results were as shown below.
| Amount
spent Number of students |
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| Less
than $20.00 5 |
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| $21.00-$40.00 7 |
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| $41.00-$60.00 2 |
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| $61.00
+ 1 |
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| Your
task is to present visually a summary of the findings in the form of a
histogram. |
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3
This year, the
first-year enrolment in a psychology class was 425 students, of which 31 were
foreign students. Compute the foreign to local students' ratio and the
percentage of foreign students in this class.
4
In
the psychology class reported in Exercise 3, 230 students were female. What is
the ratio of female to male students? What is the percentage of male and of
female students?
5
The individual test scores in the end-of-session
examination in Sociology 1 were as follows:
56, 34, 78, 98, 75, 86, 81, 67, 73, 69, 65, 86, 91, 58, 95, 78, 55, 84,
54, 73, 58, 77, 94, 66, 69, 63, 86, 72, 74, 83, 59, 88, 62, 82, 66, 46, 87, 49,
95, 48, 67, 48, 97, 49, 63, 56, 90, 68.
Compute the mean and explain its meaning within the distribution.
6
In the
data set of the previous example, compute the mean, mode and the median.
7
For the data set in Exercise 5 compute the
variance, standard deviation and the range. What do the range and standard
deviation tell us about the data?
8
During
the previous semester, 15 students completed Introductory Psychology and
Introductory Sociology. Their results in each discipline (out of 10) were as
follows:
Psychology: 4,
6, 8, 7, 9, 4, 6, 5, 7, 6, 6, 7, 6, 5, 6.
Sociology:
6, 8, 7, 9, 8, 7, 8, 6, 7, 4, 5, 3, 4, 7, 6.
Compute the mean, range, standard deviation, and z-scores
for both data sets. What can you say about the overall performance of these two
classes and the relevant disciplines?
9 In a recent study, 1500 males and females
of the same age group (in equal numbers) were asked to state their educational
status by indicating whether they had completed tertiary studies or not. The
results are given in the following table:
| Completed
tertiary studies |
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| Yes | No | Total |
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| Males | 612 | 220 | 832 |
| Females | 138 | 530 | 668 |
| Total | 750 | 750 | 1500 |
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| Use Phi (f)
to estimate the relationship between tertiary studies and gender. |
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10 A married couple was asked to rank the ten
major political parties, by setting them within a range of 1 (the most
preferable) to 10 (the least preferable). The ranking of the husband and the
wife are shown separately below. Are the rankings correlated?
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| Parties | Husband | Wife | |
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| Liberal | 1 | 2 | |
| Labour | 5 | 4 | |
| National | 2 | 1 | |
| Country | 3 | 3 | |
| Democratic | 4 | 5 | |
| Socialist | 9 | 8 | |
| Green | 6 | 7 | |
| Communist | 10 | 9 | |
| Radical | 8 | 10 | |
| Christian Union | 7 | 6 | |
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| Conduct
a correlation test to estimate the relationship between the variables in
question. |
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11
Students of a history class were asked to state
how many hours they had studied the day before the last test. Their responses
were collated with the test scores (1 to 10), both of which are given below:
| Student | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | |||||
| Hours | 4 | 6 | 8 | 9 | 5 | 2 | 5 | 9 | 6 | 7 | 6 | 4 | 7 | 6 | 9 | |||||
| Score | 6 | 8 | 6 | 5 | 6 | 4 | 7 | 4 | 4 | 8 | 5 | 6 | 9 | 4 | 7 |
TASKS: Use Pearson's correlation coefficient to test the association
and construct a scattergram.
QUESTION: Is there a correlation between hours of study and test
performance? Are the results of Pearson's r and of the scattergram consistent?
12
A study on marital power explored among other
things two issues: the degree to which spouses accepted the power system of
their marriage and the degree of marital satisfaction. The question here was
about whether high acceptance of the power system of marriage was associated
with high marital satisfaction. The answers of the first ten respondents to
these two questions are given below. Scores range from 1 (low) to 9 (high):
| Spouse | A | B | C | D | E | F | G | H | I | J | ||||||||||
| Acceptance | 7 | 8 | 5 | 7 | 4 | 6 | 8 | 3 | 7 | 6 | ||||||||||
| Satisfaction | 8 | 9 | 4 | 6 | 5 | 7 | 7 | 2 | 8 | 6 |
1
Construct a scattergram.
2
Compute Pearson's r.
3
How consistent are
the findings of the scattergram with Pearson's correlation coefficient?
13
Of the 38 students
who were admitted to the Bachelor of Arts this year, 15 decided to major in
psychology, 11 in history, and 12 in sociology. Are these differences in
choosing the field of study statistically significant?
14
A study of same-sex and other-sex couples revealed
that the degree of commitment (high, low) to their relationship is as follows:
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| Couples | High degree | Low degree | Total |
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| Same-sex | 65 | 42 | 107 |
| Other-sex | 57 | 50 | 107 |
| Total | 122 | 92 | 224 |
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| On the basis of these figures, what
can be concluded about the level of commitment of these two groups of couples?
Are the differences in commitment identified in this study significant? |
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15
In the above example,
compute the f coefficient
and Cramer's V. What can you conclude from these findings?
16
In a recent study, 25
farm wives were interviewed to determine the level of satisfaction with their
marriage. Rated between, 1 (very low) and 9 (very high), their responses were as
follows: 4.5, 5.3, 6.1, 6.3, 5.8, 8.3, 7.8, 5.6, 8.1, 6.8, 6.4, 6.1, 6.3, 5.9,
5.6, 4.4, 6.6, 7.4, 6.6, 5.7, 5.5, 7.3, 6.7, 7.4, 6.3. Knowing that the average
marital satisfaction score among city wives was found to be 6.2, what can you
conclude from this study?
17
A medical
practitioner wanted to test the
effectiveness of a new medicine for the fear of flying. The study conducted for
this purpose included two matched samples of respondents who sought relevant
medical treatment. One sample was given the new medicine Flyflex, and the other
a placebo, and in due time were subjected to a flying test. Following the test
both groups were tested using an appropriate instrument. The results of the
study are given below:
Flyflex: 3, 2, 3, 3, 4, 3, 2, 1, 2,
1, 2, 5, 6, 5, 4, 7, 6, 4, 5, 6, 3, 5, 4, 3, 5
placebo: 4, 3, 4, 4, 5, 4, 3, 2, 3,
2, 3, 6, 7, 6, 5, 7, 7, 5, 6, 7, 4, 6, 5, 4, 7
On
the basis of these findings, can you argue that Flyflex is effective?
18
Three groups of
students (N = 20 each), one from a large city, one from a small town and one
from a remote area were tested to determine their overall scholastic
achievement. The students were matched according to social and family
background. The scores of the three groups are shown below.
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| Scores
by group of respondents |
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| City | Town | Remote |
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| 5 | 6 | 6 | |
| 6 | 7 | 8 | |
| 7 | 8 | 6 | |
| 5 | 6 | 9 | |
| 6 | 7 | 5 | |
| 4 | 5 | 6 | |
| 5 | 7 | 3 | |
| 4 | 9 | 5 | |
| 6 | 8 | 4 | |
| 5 | 7 | 6 | |
| 7 | 8 | 3 | |
| 6 | 6 | 4 | |
| 5 | 7 | 2 | |
| 6 | 8 | 4 | |
| 4 | 7 | 3 | |
| 7 | 9 | 5 | |
| 5 | 6 | 4 | |
| 6 | 7 | 6 | |
| 5 | 5 | 5 | |
| 4 | 6 | 8 | |
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| Are the differences between the
scores of the three groups of students significant? Can you say that students'
test results vary according to their place of residence? |
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