Question

In a representative sample of 794 coffee growers from Country​ X, 418 growers were certified to sell to organic coffee markets while 59 growers were transitioning to become organic certified. In Country​ Y, 64​% of coffee growers are organic certified. Is there evidence to indicate that fewer than 64​% of the coffee growers in Country X are either organic certified or transitioning to become organic​ certified? State your conclusion so that there is only a 10​% chance of making a Type I error.

What are the hypotheses for this​ test?

A. H0​: p<0.64

Ha​: p=0.640

B. H0​: p=0.64

Ha​: p≠0.64

C .H0​:p≠0.64

Ha​: p=0.64

D.H0​: p > 0.64

Ha​: p or ≤ 0.64

E. H0​: p=0.64

Ha​: p > 0.64

F. H0: p=0.64

Ha: p<0.64

Answer 1

Given that, n = 794 and x = 418

sample proportion = x/n = 418/794 = 0.5264

The null and the alternative hypotheses,

H₀ : p = 0.64

H_a : p < 0.64

The test statistic is,

Z = -6.67

p-value = P(Z < -6.67) = 0.000

Reject the null hypothesis because the p-value is less than the probability of making a Type I error. Therefore, there is not sufficient evidence to indicate that fewer than 64% of the coffee growers in Country X are either organic certified or transitioning to become organic​ certified.