**Winter 2004**

** **

**Answers for
Computer Problem Set 1**

1. (b). For LIVING ARRANGEMENTS, close to one-half
of respondents live with parents or other relatives (39.7 + 7.9 = 47.6),
fifteen per cent live with a spouse or partner and close to one-fifth (18.7%)
live with friends. These are the most
common types of living arrangements.
Less than ten per cent live alone or on campus or are single with
children.

For this sample,
respondents are spread across all four years but with first and third year more
heavily represented than second and fourth year. There are also a number of fifth or higher year students, perhaps
including some graduate students. Close
to one-third of respondents report being in first year, and this may be close
to the actual proportion for U of R undergraduates. But it appears that second year students may be underrepresented
in this sample – it might be expected that there are more second than third
year students. Third year students, at
over one-quarter of the total (26.5%) may be overrepresented in this sample.

Respondents to this
sample appear to take quite a hard line on social assistance, with two-thirds
stating that social assistance should be cut if recipients do not look for work
or should look after themselves (65.4 + 3.5 = 68.9%). In contrast, only seventeen per cent consider that social
assistance should be increased and fourteen per cent consider social assistance
payments about right.

2. (b). Responses to each of the statements in V5,
V8, and V9, are measured on a five-point scale from strongly disagree (1) to
strongly agree (5). Respondents are
generally in favour of increasing corporate taxes (almost two thirds give
either response 4 or 5). More dollars
for health care is also supported fairly strongly with fifty per cent in
support of this (32.4 + 18.7 = 51.1%) and only fifteen per cent
disagreeing. User fees for health care
are opposed strongly, with over seventy per cent disagreeing with this and only
fourteen per cent in favour (8.9 + 4.9 = 13.8%).

Comparing the
distributions, the histograms show that the user fees distribution is most
concentrated at one end, with the greatest number of respondents at responses 1
and 2, the disagree end of the scale.
Corporate taxes is also heavily concentrated, but at responses 4 and 5,
the agree end of the scale. Responses
on more dollars for health care are more spread out across categories, with the
mode being the neutral response, although more agree than disagree with this.

In order to obtain the
numbers in the table at the bottom of p. 1 of the *Report*, the per cent in the middle is the neutral response of 3. In the table, the % agreeing is the sum of
the percentages in categories 4 and 5 (agree end of the scale). while the %
disagreeing is the sum of the percentages of respondents in the categories 1
and 2 (disagree end of the scale).

3. From the histograms, it is fairly apparent that third and fourth year students spend more time studying than do first and second year students. The distributions for first and second year students are very similar, with relatively few studying the least numbers of hours but with a lot studying between about 3 and 12 hours weekly, and considerable also studying between 12 and 22 hours weekly. After that, there are relatively fewer students at each larger number of hours spent studying. For third and fourth year students, the distributions are shifter a bit more to the right, with smaller percentages of students studying few hours and larger percentages studying more hours. For fifth and higher year students, hours reported studying are even greater. For first year and second year students the distribution of hours is more concentrated at lower numbers of hours, whereas for upper years the distributions are more dispersed across the different numbers of hours. (In order to see this, check the relative size of the standard deviations across the years).

From the stem-and-leaf display, for second year students, the mode if at 10 hours studying, since there are more values there (21) than at any other hour. For fourth year students, there seem to be three modes, 5, 15, and 20 hours, since there are 12 cases at each of these three hours, more than any other value.

For the median for second year students,
there are 131 students and one-half of this is 65.5, so the 66^{th}
case is the median. Counting up the
values in the stem-and-leaf plot, there are 6 + 15 + 13 + 12 + 21 = 67 values
by the time all the 10s are considered.
The 66^{th} value is one of these 10s, so the median is 10. For fourth year, there are 114 respondents,
so the 57^{th} and 58^{th} cases are the median. These are 48 cases up to 14 (6 + 23 + 19 =
48). Then there are 12 respondents
reporting exactly 15 hours studying, so the 57^{th} and 58^{th}
cases are among these. The median is 15
hours studying weekly for fourth year students. These values match with the medians reported in the *Descriptives*
box.

4. (b).
The table provides the interquartile ranges (IQR), the difference
between the 7^{th} and 25^{th} percentile – the latter appear
on the printout when the quartiles are checked in the *Statistics*
box. For these data, the IQR may not be
such a useful measure since the values are the same for each of the three
variables.

Variable |
P75 |
P25 |
IQR = P75 – P25 |

UM1 |
4 |
3 |
1 |

UM3 |
5 |
4 |
1 |

UM4 |
3 |
2 |
1 |

The distributions for UM1 (university has made me more accepting) and UM3 (U of R promotes understanding) are similar in that the two means are very close (3.40 and 3.49), and the quartiles and IQR are the same. For each of these distributions, about one-third of respondents were neutral but 40-50% agreed and only 13-18% disagreed. Responses to UM3 were a little more positive than for UM1, so the median is greater for UM3 than UM1. Also, responses to UM1 were a little more spread out, so the standard deviation is greater than for UM3.

For UM4, more visible minority students, respondents were much less in agreement, with almost forty per cent (21.3 + 17.8 = 39.1%) disagreeing and only 16.8% agreeing. This produced a mean of only 2.61, on the disagree side of a neutral response of 3. The median and quartiles are also considerably lower than for UM1 and UM3.

While UM1 and UM3 seem relatively consistent with each other, in that respondents reported becoming more accepting and consider the University to promote this, respondents do not appear to be supportive of more visible minority students at the University. This may lead one to question the type of acceptance respondents have, although if more visible minority students come to the University, they might be accepted in the same way non-visible minority students are. But this latter is only speculation.

5. (b). This continues the analysis of hours spent at various activities (see question 3) but focuses on more activities than just studying. Other than hours spent at jobs, mean study hours per week are much greater than any other activity, at 16.6, approximately three times as great as mean hours spent caring for dependents and housework. The mean time spent at jobs is greater than any other activity, at over 20 hours per week. From these data, if the means are summed, they total just over 50 hours – 20 at jobs, 16 at studying, and 14 or 15 at other activities.

While the activities with greater mean generally have larger standard deviations, the one exception is care of dependents. It appears this activity is much more variable than any other, meaning that some spend little time caring for dependents while others spend a lot of time doing so.

From these data, it appears that students generally spend considerable time at jobs, studying, and other activities during the week. But there are major differences among students as shown by the high variability in time spent at activities such as care of dependents.

Last edited February 7, 2004