Question

Various studies indicate that approximately 9% of the world's population is left handed. You think this number is actually higher. You take an SRS of 221 people and find that 22 of them are left handed. Test your claim at the 5% significance level. Part a: State your null and alternative hypotheses.

a) H0: p = 0.09; Ha: p > 0.09 b) H0: p = 0.09; Ha: p < 0.09 c) H0: p = 0.09; Ha: p ≠ 0.09

part b

Part b: State the rejection region.

a) z < −1.282 or z > 1.282

b) z > 1.960

c) z > 1.645

d) z < 1.645

e) z < 1.960

Part c: Calculate the test statistic.

a) z = 2.210

b) z = −1.870

c) z = −1.016

d) z = 0.496

e) z = 0.100

Part d: Determine the P-value for your test.

a) p-value = 0.620

b) p-value = 0.310

c) p-value = 0.155

d) p-value = 0.690

e) p-value = 0.380

Part e: State your conclusion for your hypothesis test.

a) Fail to reject the null hypothesis. There is not enough evidence to conclude that the proportion of left handers is higher than 9%.

b) Reject the null hypothesis which states which states that the world's population of left handed people is 9% in favor of the alternate which states it is actually higher.

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

Answer 1

The statistical software output for this problem is :

H₀ : p = 0.09
H_A : p > 0.09

c) z > 1.645

d) z = 0.496

b) p-value = 0.310

a) Fail to reject the null hypothesis. There is not enough evidence to conclude that the proportion of left handers is higher than 9%.