Question

Health insurance benefits vary by the size of the company. The sample data below show the number of companies prowiding health insuranc for small, medium, and large companies. For purposes of this study, small companies are companies that have fewer than 100 cmployecs. Medium-szed companics have 100 to0mploycos, and largc companics have 1,0oD or morc cmployccs The questionnaire sent to 225 employees asked whether or not the employee had heath insurance and then asked the employee to indicate the size of the company, sizc of the Company Small Medium Large 68 Heulth Irisurance 39 91 No (a) conduct ฮ test of independence to determine whether health insurance coverage is independent of the size of the company. State the null and alternative hypotheses : Having haalth insuranca is nat indapandent af the siza of tha company. Having health insurance is independent of the size cf the company, 。Mg: Havinq health insurance is independent or the size of the company. : The proportion of companies with health insurance bonafits is equal for small, medium and large companies. H: Having haalth insuranca is nat indapandent af the siza of tha company : The proportion of companies with health insurance benefits is not equal for small, medium and large companies. M Having health insurance is independent of the size of the company, H: Having health insurance is not indepandent of the sze of the company Find the velue of the test statistic. (Round your ariswer to three detimal plaves. what is the p-valuer (Round your answer to four decimal places, p-value - Uing a 0.05 level of significance, what is your contlusion Relect HO, we oondude health insurance coverage is not independent of the size of the company, Do not reject H we cannot condlude health insurance coverage is independent of the size of the company Reject We condlude health insurance coverage is independent of the size of the company Do not reject Ho We canot oncdude health insurence coveae and the size of Lhe comp e independent b A newspaper d' tic e indicated er iployees v sma companies are mure likely u ack hed h nsurance ouverage. Use percentdges besed on the above da d support this conclus on Round our answers u he neal 쁘 nte er For small companies conclusion that small companies arc loss % do not provide health insurance. For medium companies % do not provide health insurance. Hor large companies. % do not provide health insurance. I hese percentages support the likely to provide health insurance coverage when compared to medium and large companies.

Answer 1

a)Ho ..is independent of the size

Ha.,..not independent

applying chi square test:

Observed	Oi	small	medium	large	Total
	Yes	39	68	91	198
	No	11	7	9	27
	Total	50	75	100	225
Expected	Ei=row total*column total/grand total	small	medium	large	Total
	Yes	44.00	66.00	88.00	198
	No	6.00	9.00	12.00	27
	Total	50	75	100	225
chi square    χ2	=(Oi-Ei)2/Ei	small	medium	large	Total
	Yes	0.5682	0.0606	0.1023	0.731
	No	4.1667	0.4444	0.7500	5.361
	Total	4.735	0.505	0.852	6.092

test statistic =6.092

p value =0.0475

reject Ho; we conclude,,,not independent

b)

for small companies ..22% ..for medium companies 9% ...For large companies,,,9%...