Question

Various studies indicate that approximately 8% of the world's population is left handed. You think this number is actually higher. You take an SRS of 228 people and find that 28 of them are left handed. Test your claim at the 5% significance level.

State your conclusion for your hypothesis test.

a) Reject the null hypothesis which states which states that the world's population of left handed people is 8% in favor of the alternate which states it is actually higher.

b) There is not enough information to make a conclusion.

c) Fail to reject the null hypothesis. There is not enough evidence to conclude that the proportion of left handers is higher than 8%.

Answer 1

To Test :-

H0 :- P = 0.08
H1 :- P > 0.08

P = X / n = 28/228 = 0.1228

Test Statistic :-
Z = ( P - P0 ) / √ ((P0 * q0)/n))
Z = ( 0.122807 - 0.08 ) / √(( 0.08 * 0.92) /228))
Z = 2.3826

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Z(α) = Z(0.05) = 1.645
Z > Z(α) = 2.3826 > 1.645, hence we reject the null hypothesis
Conclusion :- We Reject H0

a) Reject the null hypothesis which states which states that the world's population of left handed people is 8% in favor of the alternate which states it is actually higher.