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 enployee to indicate the size of the company. Health Insurance Size of Company Yes No Total Small 32 18 50 Medium 63 12 75 Large 85 15 100

Health Insurance
	Size of Company	Yes	No	Total
	Small	32	18	50
	Medium	63	12	75
	Large	85	15	100

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 p-value is - Select your answer -less than .005 between .005 and .01 between .01 and .025 between .025 and .05 between .05 and .10 greater than .10 Item 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 independent Conclude health insurance coverage is not independent of the size of the company Item 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?

- Select your answer -Large companies have a higher percentage of no coverage than medium and small companies Medium companies have a higher percentage of no coverage than large and small companies Small, medium, and large companies all have roughly the same percentage of no coverage Small companies have a higher percentage of no coverage than large and medium companies Item 7

Answer 1

a)

Expected	Ei=row total*column total/grand total	Yes	No	Total
	small	40.00	10.00	50
	meidum	60.00	15.00	75
	large	80.00	20.00	100
	total	180	45	225
chi square    χ2	=(Oi-Ei)2/Ei	Yes	No	Total
	small	1.600	6.400	8.0000
	meidum	0.150	0.600	0.7500
	large	0.313	1.250	1.5625
	total	2.0625	8.2500	10.3125
test statistic X2 =		10.31
p value =		0.0058

between .005 and .01

Conclude health insurance coverage is not independent of the size of the company

b)

small	36%
meidum	16%
large	15%

Small companies have a higher percentage of no coverage than large and medium companies