Question

A candidate to the municipal elections in Sudbury claims that least 5% of the voters favors his party. A random sample of 500 voters in the city revealed that 22 of them were planning to vote for him

At a significance level α = 0.05, can you infer that the candidate's claim is false?

Answer 1

To Test :-

H0 :- P ≥ 0.05
H1 :- P < 0.05

P = X / n = 22/500 = 0.044

Test Statistic :-
Z = ( P - P0) / √(P0 * q0 / n)
Z = ( 0.044 - 0.05 ) / √(( 0.05 * 0.95) /500)
Z = -0.616

Test Criteria :-
Reject null hypothesis if Z < -Z(α)
Z(α) = Z(0.05) = 1.645
Z > -Z(α) = -0.6156 > -1.645, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

No, candidate's claim is not false.