Question

A private Health Clinic manager will buy the flu vaccine. There are 3 vaccines belonging to separate companies in the market and the manager wants to choose the most effective of them. He conducted a research for this and applied all the vaccines and found the results as in the table below. Is there a difference between these 3 vaccines in terms of Protecting or not Protecting against Flu disease? Alpha = 0.05 error level?

vaccine types of companies	protecting	not protecting	Total
A Company vaccine	82	42	124
B Company vaccine	70	25	95
C Company vaccine	45	20	65
Total	197	87	284

Answer 1

A private Health Clinic manager will buy the flu vaccine. There are 3 vaccines belonging to separate companies in the market and the manager wants to choose the most effective of them. He conducted a research for this and applied all the vaccines and found the results as in the table below. Is there a ? Alpha = 0.05 error level?

vaccine types of companies	protecting	not protecting	Total
A Company vaccine	82	42	124
B Company vaccine	70	25	95
C Company vaccine	45	20	65
Total	197	87	284

let us consider the null and alternative hypothesis is

Ho : there is no difference between these 3 vaccines in terms of Protecting or not Protecting against Flu disease.

Ha: there is a difference between these 3 vaccines in terms of Protecting or not Protecting against Flu disease

we have

Chi-Square Test
Observed Frequencies
	Column variable			Calculations
vaccine types of companies	protecting	not protecting	Total		fo-fe
A Company vaccine	82	42	124		-4.01408	4.014085
B Company vaccine	70	25	95		4.102113	-4.10211
C Company vaccine	45	20	65		-0.08803	0.088028
Total	197	87	284
Expected Frequencies
	Column variable
vaccine types of companies	protecting	not protecting	Total		(fo-fe)^2/fe
A Company vaccine	86.01408	37.98592	124		0.187328	0.42418
B Company vaccine	65.89789	29.10211	95		0.255355	0.578217
C Company vaccine	45.08803	19.91197	65		0.000172	0.000389
Total	197	87	284
Data
Level of Significance	0.05
Number of Rows	3
Number of Columns	2
Degrees of Freedom	2
Results
Critical Value	5.991465
Chi-Square Test Statistic	1.445641
p-Value	0.485381
Do not reject the null hypothesis

since the value of chi square test is 1.4456 and p value is 0.4854 which is greater than 0.05 so we do not reject the null hypotheses and conclude that there is no difference between these 3 vaccines in terms of Protecting or not Protecting against Flu disease.