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Health insurance benefits vary by the size of the company. Thesample data below show the number of companies providing healthinsurance for small, medium, and large companies. For purposes ofthis study, small companies are companies that have fewer than 100employees. Medium-sized companies have 100 to 999 employees, andlarge companies have 1,000 or more employees.

The questionnaire sent to 225 employees asked whether or not theemployee had health insurance and then asked the employee toindicate the size of the company.

Health Insurance	Size of theCompany
	Small	Medium	Large
Yes	30	59	82
No	20	16	18

(a)

Conduct a test of independence to determine whether healthinsurance coverage is independent of the size of the company.

State the null and alternative hypotheses.

H₀: Having health insurance is notindependent of the size of the company.
H_a: Having health insurance is independent ofthe size of the company. H₀: Having healthinsurance is not independent of the size of the company.
H_a: The proportion of companies with healthinsurance benefits is not equal for small, medium and largecompanies.     H₀:Having health insurance is independent of the size of thecompany.
H_a: The proportion of companies with healthinsurance benefits is equal for small, medium and largecompanies.H₀: Having health insurance isindependent of the size of the company.
H_a: Having health insurance is not independentof the size of the company.

Find the value of the test statistic. (Round your answer tothree decimal places.)

What is the p-value? (Round your answer to four decimalplaces.)

p-value =

Using a 0.05 level of significance, what is your conclusion?

Do not reject H₀. We cannot conclude healthinsurance coverage and the size of the company are notindependent.Do not reject H₀. We cannotconclude health insurance coverage is independent of the size ofthe company.     RejectH₀. We conclude health insurance coverage isindependent of the size of the company. RejectH₀. We conclude health insurance coverage isnot independent of the size of the company.

(b)

A newspaper article indicated employees of small companies aremore likely to lack health insurance coverage. Use percentagesbased on the above data to support this conclusion. (Round youranswers to the nearest integer.)

For small companies,  % do not provide healthinsurance. For medium companies,  % do not provide healthinsurance. For large companies,  % do not provide healthinsurance. These percentages support the conclusion that smallcompanies are  ---Select--- less more equally likely toprovide health insurance coverage when compared to medium and largecompanies.