Question

The chi-square test for independence - 2 x 2

Individuals with strong religious beliefs often turn to their faith to cope with stressful life events. Relying on God’s love and caring is referred to as positive religious coping.

Andrea Phelps and her colleagues studied the relationship between positive religious coping and the type of care received by terminally ill cancer patients. Most of the patients in the study were Christian. [Source: Phelps, A. et al., “Religious coping and use of intensive life-prolonging care near death in patients with advanced cancer.” Journal of the American Medical Association, 301 (2009): 1140–1147.]

Suppose another researcher conducts a similar study but uses a sample of patients whose religious traditions are more varied than the patients in the Phelps study. She samples 200 terminally ill patients to see whether their practicing a religion is related to how likely they are to have a do-not-resuscitate order.

The following table shows the results of the study.

Observed Frequencies

	Do-Not-Resuscitate Order
Practices a Religion	Yes	No
Yes	65	19
No	55	61

1. Given these data, the most appropriate test to use to check whether there is a significant relationship between whether terminally ill patients practice a religion and whether they have a do-not-resuscitate order is a(n) _______________________ .

2. To do this test, which of the following assumptions and/or restrictions are required? Check all that apply.

a.The observations must be independent.

b.The population sampled must be normal.

c.The smallest expected frequency must be greater than 5% of the total sample.

d.The smallest expected frequency must be at least five.

3. The researcher’s null hypothesis is: “Among terminally ill patients, there is no relationship between whether they practice a religion and whether they have a do-not-resuscitate order.” Fill in the following table of expected frequencies.

	Expected Frequencies
	Do-Not-Resuscitate Order
Practices a Religion	Yes	No
Yes
No

4. The chi-square statistic is _________ .

5. The distribution of the chi-square statistic has ____________ degree(s) of freedom.

Use the Distributions tool to answer the following questions.

6. With α = 0.05, the critical value is ____________ .

7. Because the chi-square statistic _____________ the critical value, the researcher__________ the null hypothesis and concludes that there ______________ convincing evidence of a significant relationship between whether terminally ill patients practice a religion and whether they have a do-not-resuscitate order.

Answer 1