Health insurance benefits vary by the 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 the purposes of this study, small companies are companies that have fewer than employees. Medium-sized companies have to employees, and large companies have or more employees. The questionnaire sent to employees asked whether or not the employee had health insurance and then asked the enployee to indicate the size of the company.
Health Insurance
Size of Company Yes No Total
Small 35 15 50
Medium 68 7 75
Large 86 14 100
Required:
a. Conduct a test of independence to determine whether health insurance coverage is independent of the size of the company. What is the p-value? Compute the value Of the X2 test statistic (to 2 decimals).
b. A newspaper 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).