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Exercises



1.
In a study of drug usage by students at a large university, data was obtained regarding hard liquor experience of smokers and nonsmokers.

Hard-liquor use Nonsmokers Smokers
Once or more 15 23
Never 56 18

Conduct a test of significance to assess whether liquor experience is independent of smoking.

2.
A study investigating the association between size of cars and country found the following frequency counts:
  USA Japan UK France
Economy 21 24 33 55
Compact 27 35 37 40
Full Size 36 11 12 4
Luxury 15 3 7 8
Is there evidence of a significant relationship between size of car and country, or are the two variables independent?

3.
To compare two diets (A and B), a study was done where overall health was measured as either excellent, average, or poor. The frequencies are listed in the following table. Does the data suggest that health depends on diet, or are they independent?
  Excellent Average Poor
Diet A 37 24 19
Diet B 17 33 20

4.
Are hard-driven, intense people (said to possess Type A personality) more inclined to heart problems than those with low-key, easy going Type B personalities? A study was made involving 510 heart attack patients. An activity survey test was given to determine Type A, Type B, and neutral personalities. Each person's case was followed for three years and the number who survived for three years after the heart attack were recorded. The data follow:
  Type A Neutral Type B
Died 20 15 15
Survived 160 150 150

(a)
Do the data provide sufficient evidence to indicate that survival rates are different for different types of people?
(b)
Suppose that a larger study resulted in the following table:
  Type A Neutral Type B
Died 40 30 30
Survived 320 300 300
Observe that all the frequencies in the larger study are twice the size of the first study. Do you expect the P-value of the larger study to be smaller, larger, or approximately equal to the first study?

5.
In April 2003, a researcher conducted a survey to test for association between opinions on gun control and war with Iraq. She asked 100 people two questions: (i) do you believe that private citizens should be allowed to own guns, and (ii) did you approve of the decision to send troops to Iraq? The marginal totals are given below.

  Yes on troops No on troops Total
Yes on guns     40
No on guns     60
Total 51 49 100

(a)
Compute the table of Expected Frequencies.
(b)
Suppose 25 respondents answered 'Yes' to both questions. Calculate the chi-square test statistic for independence/association between the two opinions.
(c)
Use the chi-square curve to compute the P-value for your test statistic above. What is the correct degrees of freedom to use?
(d)
What is the conclusion of your test?

6.
Computer-controlled cameras are being used to ticket automobile drivers for speeding and running red lights. These devices are operated by private firms and have an incentive to pull in as many drivers as they can. Although approximately 70 accept and pay these tickets, others resent this procedure and fight the ticket. A frequency table with marginal totals is given below. Assume that the actions of 200 motorists who received a ticket from a computer-controlled camera produced the following results. Is there evidence of a significant difference between the proportions of motorists who pay their ticket by the type of traffic violation?
  Run red light Speeding Total
Pay ticket     140
Fight Ticket     60
Total 60 140 200

(a)
Compute the table of Expected Frequencies.
(b)
Suppose we know that 1/3 of those who were ticketed for running a red light fought the ticket. Is this enough information to conduct a test of association/independence between the two variables?
(c)
Using the information in (b), compute the chi-square test statistic for independence/association between the two variables.
(d)
Use the chi-square curve to compute the P-value for your test statistic above. What is the correct degrees of freedom to use?
(e)
What is the conclusion of your test?


next up previous contents index
Next: Correlation Up: Testing Equality of Frequencies Previous: Calculating a Chi-Square Test

2003-09-08