Question

Out of the 75 patients admitted to a hospital with Hepatities symtoms, 40 were administered a certain new drug, of these 34 recovered. Of the remaining who were give the traditional drug, 19 recovered. Test at 5% and 1% level of significance that the new drug is an improvement over the traditional drug.

Answer 1

H₀: Type of drug and recovery from the disease are independent. 

H₁ : Type of drug and recovery from the disease are dependent. 

The test statistic is –

The given data can be presented in 2 × 2 contigency table as below:

\(X^2 =\frac {75(34\times 16-6 \times19)^2}{40\times35\times53 \times22}\)

χ²_cal = 8.495 

At 5% level: for 1 d.f at 5% level of significance the upper tail critical value is K = 3.84. 

Here χ²_cal = 8.495 is in rejection region/χ²_cal > χ²_tab 

∴ H₀ rejected and H₁ is accepted.

At 1% level : Here K = 6.63 

Here χ² cal = 8.495 is in rejection region/ χ²_cal > χ²_tab 

∴ H₀ rejected and H₁ is accepted. 

Conclusion: type of drug and recovery from the disease are dependent, t – Tests.