Question

1. These questions pertain to Table 1.

a. How many chi-square tests of independence are performed? What are each of the bivariable associations tested [list 2 pairs of associations]?

b. Which of the relationships are significant?

c. In everyday language, describe what is shown about the relationship between age and type of drinking (light/moderate) among all students? Among drinkers only?

d. How many degrees of freedom are there in the analysis of religion by type of drinker among all students? Show how you arrive at this answer.

e. Identify the critical value from the chi-square distribution associated with the degrees of freedom in 1d.

Table 1 Chi-Square Results of the Percent of Students Exhibiting Each Quantitity- Frequency Level for ALL STUDENTS, and for DRINKERS ONLY within Personal Demographic Characteristics". DRINKERS ONLY ALL STUDENTS н L/M # н L/M # A Gender 43.1* 56.9 3630 33.7* 44.5 21.8 4641 Males Females 17.9 5071 82.1 12.4 56.7 7440 30.9 Race 30.4* 69.6 7544 23.2* 53.3 23.5 9862 White 15.9 84.1 1045 8.6 45.8 1921 45.6 Non-White Age 31.6* 4841 68.4 22.1* 47.7 30.2 6931 Under 21 75.6 24.4 3868 57.7 18.6 23.7 5068 Over 21 Religious Background Catholic 33.2* 66.8 3244 28.0* 56.4 15.6 3844 28.9 197 71.1 24.4 59.8 15.8 234 Jewish Protestant 27.3 72.7 2561 21.1 56.4 22.4 3301 drinkers Protestant, 22.3 77.7 1348 11.6 40.4 48.0 2594 non drinkers Importance of Religion Very 24.9*34.1 75.1 5315 16.7* 50.4 32.9 7923 65.9 3348 55.4 28.7 16.0 3985 Not = Number of students, A=Abstain, L/M=Light/Moderate, H=Heavy # p<.001 Note: sample size in each category does not necessarily add up to the total sample +p<.05

Answer 1

a) Total 10 chi-square tests of independence are performed (five on each category).

* Gender with frequency levels of all students, *Gender with frequency levels of Drinkers only

* Race with frequency levels of all students, *Race with frequency levels of Drinkers only

b) All the demographic variables are significantly (p<0.001) associated with frequency levels of all students and also frequency levels of drinkers only.

c) Age was found to be significantly associated with different frequency levels of all students and also with different frequency levels of drinkers only. i.e. age is depend on frequency levels of all students and drinkers only.

d) d.f = (r-1)*(s-1) = (4-1)*(2-1) = 3

Here in religion, the number of rows = 4

number of columns = 2

e) At alpha=0.05 level with '3' degrees of freedom the chi-square critical value = 7.82