Question

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

Answer 1

H0: Type of and recovery from the *** are independent.

H1 : Type of and recovery from the *** 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})

χ2cal = 8.495

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

Here χ2cal = 8.495 is in rejection region/χ2cal > χ2tab

∴ H0 rejected and H1 is accepted.

At 1% level : Here K = 6.63

Here χ2 cal = 8.495 is in rejection region/ χ2cal > χ2tab

∴ H0 rejected and H1 is accepted.

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