Social Studies 201
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?