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 100 employees. Medium-sized companies have 100 to 999 employees, and large companies have 1000 or more employees. The questionnaire sent to 225 employees asked whether or not the employee had health insurance and then asked the employee to indicate the size of the company.

		Health Insurance
	Size of Company	Yes	No	Total
	Small	31	19	50
	Medium	63	12	75
	Large	86	14	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).

b. A newspaper article indicated employees of small companies are more likely to lack health insurance coverage. Calculate the percentages of employees without health insurance based on company size (to the nearest whole number).

Small
Medium
Large

Answer 1

a)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Yes	No	Total
	Small	40.000	10.000	50.00
	Medium	60.000	15.000	75.00
	Large	80.000	20.000	100.00
	total	180.00	45.00	225.00
chi square    χ2	=(Oi-Ei)2/Ei	Yes	No	Total
	Small	2.025	8.100	10.1250
	Medium	0.150	0.6000	0.7500
	Large	0.450	1.8000	2.2500
	total	2.6250	10.5000	13.125
test statistic X2 =		13.13

p value =

0.0014 or less than 0.01

b)

Small	38%
Medium	16%
Large	14%

small companies have a higher percentage of no coverage than large and medium companies