Answered: In a representative sample of 833…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

In a representative sample of

833

coffee growers from Country X,

468

growers were certified to sell to organic coffee markets while

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

chance of making a Type I error.

**Hypothesis Testing for Organic Certification of Coffee Growers**

In a representative sample of 833 coffee growers from Country X, 468 growers were certified to sell to organic coffee markets while 65 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.

What are the hypotheses for this test?

A. $ H_0: p = 0.67 $
$ H_a: p \neq 0.67 $

B. $ H_0: p = 0.67 $
$ H_a: p < 0.67 $

C. $ H_0: p = 0.67 $
$ H_a: p > 0.67 $

D. $ H_0: p \neq 0.67 $
$ H_a: p = 0.67 $

E. $ H_0: p > 0.67 $
$ H_a: p \leq 0.67 $

F. $ H_0: p < 0.67 $
$ H_a: p = 0.67 $

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.

\[ p\text{-value} = \]
(Round to three decimal places as needed.)

What is the conclusion of the test?

___ the null hypothesis because the p-value is ___ the probability of making a Type I error. Therefore, there is ___ evidence to indicate that fewer than 67% of the coffee growers in Country X are either organic certified or transitioning to become organic certified.

### Analysis:

The text is presenting a hypothesis test scenario to determine if the proportion of coffee growers in Country X who are certified or transitioning to organic certification is lower than the 67% certification rate in Country Y.

1. **Hypotheses (Step 1):**
- Null Hypothesis ($H_0$): $ p = 0.67 $
- Alternative Hypothesis ($H_a$): $ p < 0.67 $

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