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. The questionnaire 100 to 999 employees, and largest 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.

CENGAGE MINDTAP Q Search this course Chapter 12 Assignment eBook 5. O 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. 7. O Kolo Health Insurance Size of Company Yes No Small 33 17 Medium 66 9 75 Large 90 100 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 x2 test statistic (to 2 decimals). 10 The p-value is - Select your answer Using a = .05 level of significance, what is your conclusion? - Select your answer - 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 - Check My Work

Answer 1

Ans:

a)

	Observed(fo)
	Yes	No	Total
Small	33	17	50
medium	66	9	75
Large	90	10	100
Total	189	36	225
	Expected(fe)
	Yes	No	Total
Small	42	8	50
medium	63	12	75
Large	84	16	100
Total	189	36	225
	Chi square=(fo-fe)^2/fe
	Yes	No	Total
Small	1.93	10.13	12.05
medium	0.14	0.75	0.89
Large	0.43	2.25	2.68
Total	2.50	13.13	15.63

Chi square=15.63

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

p-value=CHIDIST(15.63,2)=0.0004

As,p-value is less than 0.05,we reject the null hypothesis.We can conclude that health insurance is not independent of the size of the company.

b)

Percentage for small=100*17/50=34%

Percentage for medium=100*9/75=12%

Percentage for large=100*10/100=10%

Yes,Small companies are more likely to lack health insurance.