With doubledigit annual percentage increases in the cost of

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 31 19 50 Medium 64 11 75 Large 85 15 100

a,Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use = .05. Compute the value of the 2 test statistic (to 2 decimals). The p value is What is your conclusion?

b,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?

Solution

a.
a = 0.05

H0: employee health insurance coverage and size of the company are independent
H1: employee health insurance coverage and size of the company are not independent

observed frequencies,f0:

expected frequencies,fe:
fe = (row total * column total) / total
for example:
fe1 = 50*180 / 225 = 40
fe4 = 75*45 / 225 = 15

test statistic,X^2 = 6.15

degree of freedom = (number of rows - 1) * (number of columns - 1) [not including total]
df = (3-1)*(2-1) = 2

P_value = 0.0462
Since P_value < 0.05, hence reject H0
So, we can not conclude that employee health insurance coverage is independent of the size of the company.
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b.
small = (16/50)*100 = 32%
medium = (14/75)*100 = 18.67 = 19%
large = (15/100)*100 = 15%

We conclude that larger the size of the company lesser is the employee health insurance coverage.