Question

Suppose that, using standard treatments, 60% of patients completely recover from a disease. A new treatment is used on a random sample of 800 individuals, and 513 completely recover. Is this evidence, at the 5% level of significance, that this new treatment can improve the recovery rate? Do a complete hypothesis test, and show all work. (included the formula)

Answer 1

To Test :-

H0 :- P = 0.60
H1 :- P ≠ 0.60

P = X / n = 513/800 = 0.6412
Test Statistic :-
Z = ( P - P0 ) / √ ((P0 * q0)/n))
Z = ( 0.64125 - 0.6 ) / √(( 0.6 * 0.4) /800))
Z = 2.3816

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Z(α) = Z(0.05) = 1.645
Z > Z(α) = 2.3816 > 1.645, hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = P ( Z > 2.3816 )
P value = 0.0086
Reject null hypothesis if P value < α = 0.05
Since P value = 0.0086 < 0.05, hence we reject the null hypothesis
Conclusion :- We Reject H0

There is sufficient evidence to support the claim that new treatment can improve the recovery rate.