Question

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 100 employees. Medium-sized companies have 100 to 999 employees, and large companies have 1000 or more employees. The questionnaire sent to 225 employees asked whether or not the employee had health insurance and then asked the employee to indicate the size of the company.

		Health Insurance
	Size of Company	Yes	No	Total
	Small	31	19	50
	Medium	61	14	75
	Large	88	12	100

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 x^2 test statistic (to 2 decimals).

The -value is - Select your answer -less than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2

Using  level of significance, what is your conclusion?

- Select your answer -Cannot reject the assumption that health insurance coverage and size of the company are independentConclude health insurance coverage is not independent of the size of the companyItem 3

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).

Small	_____ %
Medium	_____%
Large	_____%

Based on the percentages calculated above, what can you conclude?

Answer 1

(a) Here Hypothesis are

H0 : Size of the company and health insurance coverage are independent.

Ha: Size of the company and health insurance coverage are dependent.

Here expected value = Total value in row * total value in column/Total population

Size of company	Yes	No	Total
Small	40	10	50
Medium	60	15	75
Large	80	20	100
Total	180	45	225

Chi-square value= =

Size of company	Yes	No	Total
Small	2.025	8.100	10.125
Medium	0.017	0.067	0.083
Large	0.800	3.200	4.000
Total	2.842	11.367	14.208

= 14.208

dF = (2-1) * (3-1) =2

p - value = CHIDIST( > 14.208; 2) = 0.0008

p value is less than .005

(b) Here we Conclude health insurance coverage is not independent of the size of the company.

(c)

Small = 19/50 = 38 %

Medium = 14/75 = 18.67%

Large = 12/100 = 12 %