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	37	13	50
	Medium	62	13	75
	Large	90	10	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 X^2 test statistic (to 2 decimals).

The P-value is .025 and .05

Using .05 level of significance

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	42.0000	8.0000	50.00
	medium	63.0000	12.0000	75.00
	large	84.0000	16.0000	100.00
	total	189.00	36.00	225.00
chi square    χ2	=(Oi-Ei)2/Ei	yes	No	Total
	small	0.595	3.125	3.7202
	medium	0.016	0.083	0.0992
	large	0.429	2.250	2.6786
	total	1.0397	5.4583	6.498
test statistic X2 =		6.50

The P-value is between .025 and .05

b)

small	26%
medium	17%
large	10%

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