Question

A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 275 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related? Vaccination Status Diseased Not Diseased Total Vaccinated 53 17 70 Not Vaccinated 62 143 205 Total 115 160 275

Answer 1

Answer:

Step-by-step explanation:

From the give information: A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 275 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related?

Vaccination Status         Diseased         Not Diseased      Total

Vaccinated                           53                    17                      70

Not Vaccinated                    62                    143                   205

Total                                     115                     160                  275

In this study, we have two variables   ( Vaccination and diseases status ) The null and the alternative hypothesis can be stated as follows:

Null hypothesis: The two variables   ( Vaccination and diseases status ) are independent

Alternative hypothesis : The two variables   ( Vaccination and diseases status ) are dependent

The Chi-square test statistics can be computed as:

The Expected Values for the table can be calculated by using the formula:

$E_i=\dfrac{row \ total \times column \ total}{grand \ total}$

Vaccination Status         Diseased         Not Diseased      Total

Vaccinated                       29.273                 40.727              70

Not Vaccinated                85.727                 119.273             205

Total                                     115                     160                  275

$Chi - Square \ X^2 = \dfrac{(O_i-E_i)^2}{E_i}$

Vaccination Status         Diseased         Not Diseased      Total

Vaccinated                       19.232                13.823              33.055

Not Vaccinated                6.564                 45.573              52.137

Total                                  25.796               59.396             85.192

Therefore;

the Chi-Square Test Statistics = 85.192

For this study; we two rows and two columns

Therefore, the degree of freedom = (rows-1) × (columns-1)

the degree of freedom = (2 - 1) × (2 - 1)

the degree of freedom =  1 × 1

the degree of freedom =  1

Using the level of significance of ∝ = 0.05 and degree of freedom = 1 for the chi-square test

The p-value for the test statistics  = 0.00001

Decision rule: Since the P-value is lesser than the level of significance , therefore we reject the null hypothesis at the level of significance of 0.05

Conclusion:

We accept the alternative hypothesis and  conclude that the two variables

(Vaccination and diseases status ) are dependent  i.e the  vaccination and disease status are related