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. Health Insurance Size of Company Yes No Total Small 32 18 50 Medium 70 5 75 Large 87 13 100 Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use  = .05. Use Table 12.4. Compute the value of the  2 test statistic (to 2 decimals). The p value is Selectless than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2 What is your conclusion? SelectConclude health insurance coverage is not independent of the size of the companyCannot reject the assumption that health insurance coverage and size of the company are independentItem 3 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 % Based on the percentages calculated above, what can you conclude? SelectLarge companies have a higher percentage of no coverage than medium and small companiesMedium companies have a higher percentage of no coverage than large and small companiesSmall companies have a higher percentage of no coverage than large and medium companiesSmall, medium, and large companies all have roughly the same percentage of no coverageItem 7

• Check My Work

Answer 1

a)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	yes	No	Total
	small	42.000	8.000	50.00
	medium	63.000	12.000	75.00
	large	84.000	16.000	100.00
	total	189.00	36.00	225.00
chi square    χ2	=(Oi-Ei)2/Ei	yes	No	Total
	small	2.381	12.500	14.8810
	medium	0.778	4.0833	4.8611
	large	0.107	0.5625	0.6696
	total	3.2659	17.1458	20.412
test statistic X2 =		20.41

p value is less than .005

Conclude health insurance coverage is not independent of the size of the company

b)

small	36%
medium	7%
large	13%

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