Question

In a representative sample of 847coffee growers from Country​ X, 418 growers were certified to sell to organic coffee markets while 105 growers were transitioning to become organic certified. In Country​ Y, 65​% of coffee growers are organic certified. Is there evidence to indicate that fewer than 65​% 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 > 0.65

Ha​: p ≤ 0.65

B. H0: p=0.65

Ha: p < 0.65

C. H0​: p < 0.65

Ha​: p = 0.65

D.H0​: p ≠ 0.65

Ha​: p = 0.65

E. H0​: p = 0.65

Ha​: p > 0.65

F. H0​: p = 0.65

Ha​: p ≠ 0.65

Calculate the value of the​ z-statistic for this test.

z=_______ ​(Round to two decimal places as​ needed.)

Calculate the​ p-value for this test.

​p-value = ________ ​(Round to three decimal places as​ needed.)

What is the conclusion of the​ test?

( Do not reject, Reject) the null hypothesis because the​ p-value is

(less than, greater than) the the probability of making a Type I error.​ Therefore, there is

(insufficient,sufficient) evidence to indicate that fewer than 65 %of the coffee growers in Country X are either organic certified or transitioning to become organic certified.

Answer 1

Ans:

Option B is correct.

H₀: p=0.65

H_a: p < 0.65

sample proportion=(418+105)/847=0.6175

z-statistic :

z=(0.6175-0.65)/sqrt(0.65*(1-0.65)/847)

z=-1.98

p-value=P(z<-1.98)=0.024

Reject,the null hypothesis because the​ p-value is less than the the probability of making a Type I error.​

Therefore, there is sufficient evidence to indicate that fewer than 65 %of the coffee growers in Country X are either organic certified or transitioning to become organic certified.