Question

Health insurance benefits vary by the size of the company (the Henry J. Kaiser Family Foundation website, June 23, 2016). The sample data below show the number of companies providing health insurance for small, medium, and large companies. For the purposes of this study, small companies are companies that have fewer than  employees. Medium-sized companies have  to  employees, and large companies have  or more employees. The questionnaire sent to  employees asked whether or not the employee had health insurance and then asked the enployee to indicate the size of the company.

Health Insurance
	Size of Company	Yes	No	Total
	Small	35	15	50
	Medium	69	6	75
	Large	85	15	100

a. Conduct a test of independence to determine whether health insurance coverage is independent of the size of the company. What is the p-value?

Compute the value of the X² test statistic (to 2 decimals).

Answer 1

The statistical software output for this problem is :

Contingency table results:
Rows: Size of Company
Columns: None

	Yes	No	Total
Small	35	15	50
Medium	69	6	75
Large	85	15	100
Total	189	36	225

Chi-Square test:

Statistic	DF	Value	P-value
Chi-square	2	10.9375	0.0042

Test statistics = 10.94

P-value = 0.0042