In a representative sample of 871 coffee growers from Country X, 460 growers wer

Question

In a representative sample of 871 coffee growers from Country X, 460 growers were certified to sell to organic coffee markets while 94 growers were transitioning to become organic certified. In Country Y, 67% of coffee growers are organic certified. Is there evidence to indicate that fewer than 67% 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 1% chance of making a Type I error.

Calculate the value of the z-statistic for this test. (Round to two decimal places as needed.)

Calculate the p-value for this test. (Round three decimal places as needed.)

Explanation / Answer

here nullhypothesis: p=0.67

alternate hypothesis: p<0.67

std error=(p(1-p)/n)1/2 where n=871

=0.0159

phat=460/871=0.528

hence test stat z=(phatr-p)/std error =-8.9045

for above test stat ; p value =0.0000

as p value is less then 0.01 level ; we reject null hypothesis and conclude that  fewer than 67% of the coffee growers in Country X are either organic certified or transitioning to become organic certified

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