Question

With double-digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health insurance coverage (USA Today, January 23, 2004). The following sample data provide a comparison of workers with and without health insurance coverage for small, medium, and large companies. For the purposes of this study, small companies are companies that have fewer than 100 employees. Medium companies have 100 to 999 employees, and large companies have 1000 or more employees. Sample data are reported for 50 employees of small companies, 75 employees of medium companies, and 100 employees of large companies.

Size of Company	Yes	No	Total
	Small	39	11	50
	Medium	69	6	75
	Large	90	10	100

1. Compute the X²  test statistic:

2. What is the P-Value? (Using a Chi-Square table)

3.What can we conclude?

4. The USA Today 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	%

5. Based on the Calculated percentages, what can we conclude?

Answer 1

#1.

Observed
	Yes	No	total
Small	39	11	50
Medium	69	6	75
Large	90	10	100
Total	198	27	225

Expected value = sum(coli)*sum(rowi)/total

Expected
	Yes	No
Small	44.000	6.000
Medium	66.000	9.000
Large	88.000	12.000

Test statistic, chi-square = sum((Oi - Ei)^2/Ei) = 6.25

#2.

p-value = 0.0439

#3.

As p-value < 0.05, reject H0

There are significant evidence to conclude that the size of the organisation and health insurance are not independent

#4.

Small = 22.00%
Medium = 8.00%
Large = 10.00%