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 enployee to indicate the size of the company.

Health Insurance

Size of Company Yes No Total

Small 32 18 50

Medium 63    12 75

Large 85    15    100

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 x^2 test statistic

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 _____%

Based on the percentages calculated above, what can you conclude?

Answer 1

Applying chi square test:

Expected	Ei=row total*column total/grand total	Yes	No	Total
	Small	40.00	10.00	50
	medium	60.00	15.00	75
	Large	80.00	20.00	100
	total	180	45	225
chi square    χ2	=(Oi-Ei)2/Ei	Yes	No	Total
	Small	1.6000	6.4000	8.0000
	medium	0.1500	0.6000	0.7500
	Large	0.3125	1.2500	1.5625
	total	2.0625	8.2500	10.3125

test statistic X2 =		10.313
p value =		0.0058

b)

Small	36%
medium	16%
Large	15%

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