**Social Studies 201**

**Fall 2003**

**Problem Set 4**

**Due: November
3, 2003**

Note: If you wish this marked prior to the November 5 midterm, please hand in by Friday, October 31.

1.
Explain which concept of probability (theoretical, frequency, subjective)
appears to be implied by the word in bold print in each of the following
quotes.

a.
Witness
says Thatcher no **risk** to most
people. *Moose Jaw Times-Herald*, September 26, 2003, p. 1.

b.
In
a deck of cards with fifty-two cards, the **probability
**of obtaining a straight flush (five cards of the same suit in sequence) in
a poker hand of five cards is 9/649740.
(From web site *Poker Probabilities*, http://www.pvv.ntnu.no/~nsaa/poker.html).

c.
In
an article entitled “Babies in bed with adults are in peril,” it is reported
that “Babies who sleep in adult beds are 40 times more **likely** to die of suffocation than those who sleep in their own
cribs.” *The Globe and Mail*, October 6, 2003, p. A10.

d.
An
Ipsos-Reid survey of Canadian consumer confidence reported that “14 per cent of
Canadians are **likely** to buy a home
at this time.” *The Globe and Mail*, October 6, 2003, p. B6.

e.
A
recent Canada study stated that “individuals from higher-income families are
much more **likely** to attend
university.” Statistics Canada, *The Daily*, October 3, 2003, from web
site http://www.statcan.ca/Daily/English/031003/d031003b.htm

2.
From the SSAE98 data set, obtain a cross-classification (*Analyze-Descriptive Statistics-Crosstabs*) of V4, attitude
concerning marriage of gays and lesbians, by sex of respondent. Regarding this cross-classification table as
a population from which an individual is randomly selected, obtain the
following:

a.
The
probability of selecting a male.

b.
The
likelihood of selecting someone who strongly disagrees with same-sex marriage
(ssm).

c.
The
probability of selecting an individual who agrees with ssm (response 4 or 5).

d.
The
probability of selecting a female or a neutral response to ssm (3).

e.
The
chance of selecting a male and someone who has a neutral response about ssm.

f.
The
probability that the individual selected strongly disagrees with ssm, given
that the individual is a male.

g.
The
probability that the individual selected strongly disagrees with ssm, given
that the individual is a female.

h.
Are
the events of strongly agreeing with ssm and the events of being female
independent or dependent?

i.
Are
the events of having a neutral response to ssm and being female independent or
dependent?

j.
Given
your responses to f. through i., write a sentence or two describing whether
males or females are more likely to favour treating gays and lesbians as
married.

3.
In Computer Problem Set 1, question 4, you examined the relationship between
V8, support for user fees for health care, and V9, more spending for health care. The finding was that support for user fees
was limited and support for more spending was strong. While these results are consistent with each other, the data
obtained did not allow you to examine whether individuals who opposed user fees
were the same ones that supported more spending. The latter can be examined by requesting a cross-classification
of V8 by V9. Obtain this from the
SSAE98 data set and, using this table, answer the following:

a.
For
those who strongly disagree with user fees, what is the conditional probability
of strongly agreeing with more health care dollars?

b.
For
those who strongly agree with user fees, what is the conditional probability of
strongly agreeing with more health care dollars?

c.
Are
the events of somewhat agreeing (4) with V9 and the event of strongly
disagreeing with user fees independent or dependent?

d.
Are
the events of agreeing (4 or 5) with V9 and the event of somewhat agreeing with
user fees (category 4 of V8) independent or dependent?

e.
From
the above probabilities, does it appear that individuals who oppose user fees
generally express stronger support for increased health care spending?

4. Find two pairs of dependent events and one
pair of independent events in the following quotes:

“Diabetes is a
cardiovascular disease that requires early and aggressive treatment, and … the
primary culprits are dietary fat and inactivity, not sugar.” *The
Globe and Mail*, October 18, 2003, p. A1.

The adage that it pays to
get an education doesn’t apply to arts and culture graduates, according to a
new Statistics Canada study, which suggests that for them Canada is a
wasteland. Compared with other
graduates, the federal agency says “arts and culture graduates were more likely
to be moonlighting, be self-employed, earn lower pay, change employers, and
find only temporary work. (*National Post*,
March 17, 2001, p. A10).

5.
For the standardized normal distribution,

a.
What
is the area between Z of 0 and Z of +1.53?

b.
What
is the area between Z of 1 and Z of +2.12?

c.
What
is the proportion of cases between Z = -1.2 and Z = +0.7?

d.
What
percentage of the area under the normal curve lies to the right of Z=+1.75?

e.
What
is the area under the normal curve above Z=-1.08?

f.
What
percentage of population members in a normally distributed population is less
than 1.2 standard deviations above the mean?

g.
What
is the Z-value so that 0.3 of the area lies to the right of this Z?

h.
What
are the Z-values so that there is 0.04 of the area in each tail of the
distribution lying beyond these Z-values?

i.
What
is the first quartile in a standardized normal distribution?