Health insurance benefits vary by 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 purposes of this study, small companies are companies that have fewer than 100 employees. Medium-sized companies have 100 to 999 employees, and large companies have 1000 or more employees. The questionnaire sent to 220 employees asked whether or not the employee had health insurance and then asked the employee to indicate the size of the company. Conduct a test of independence to determine whether health insurance coverage is independent of the size of the company.

health insurance	small	medium	large
yes	37	74	65
no	18	16	10

a) Set up the null and alternative hypotheses for this test.

b) Calculate the expected frequencies for this test. You don't have to provide your calculations, only the table with frequencies.

c) What is the value of the test statistic for this test? Again, you don't have to list every single item you used to obtained the test statistic, only the final result.

d) At a 0.05 level of significance, what is the critical value for your test? Report the number of degrees of freedom you have for the 2 distribution.

e) What is the conclusion of your test? Don't forget to provide an interpretation of your result.

f) A newspaper article indicated employees of small companies are more likely to lack health insurance coverage. Use percentages based on the above data to support this conclusion. There is no need to conduct a formal hypothesis test to answer this part.