show work 6. In a representative sample of 817 coffee growers from Country X, 450 growers were certified to sell organic coffeemarkets while 62 growers were transitioning to become organic certified. In Country Y, 66% of coffee growers areorganic certified. Is there evidence to indicate that fewer than 66% of the coffee growers in Country X are eitherorganic certified or transitioning to become organic certified? State your conclusion so that there is only a 5%chance of making a Type I error (i.c., test using a = 0.05).(a) What are the hypotheses for this test?Ho:(b) Calculate the value of the test statistic za (round to two decimal places as needed):Hint: Before finding 2, you will first need to calculate the sample proportion p. Pay close attention to what isbeing tested. EITHER "certified" OR "transitioning" counts as a success for your proportion here.(c) Calculate the p-value (round to three decimal places as needed).You should find one of the following useful for part C:P(: < 0.66) 0.7454 P(: < -0.033) 0.4868 P(: < -2.01) 0.0222P(: < -6.59) 0(d) What is the conclusion of the test?REJECT or FAIL TO REJECT the null hypothesis because the p-value is LESS THAN or GREATER THAN theprobability of making a Type I error. Therefore, there is SUFFICIENT or INSUFFICIENT evidence to indicatethat fewer than 6% of the coffee growers in Country X are either organic certified or transitioning to becomeorganic certified. (Circle the correct capitalized word or phrase in cach of the three places a choice is given.)(e) If this were a two-tail test, with everything else the same, would your conclusion be different? Explain. 2. Pharmaceutical companies spend billions of dollars per year on research and development of new drugs. Thepharmaceutical company must subject each new drug to lengthy and involved testing before receiving the necessarypermission from the Food and Drug Administration (FDA) to market the drug. The FDA's policy is that the phar-maceutical company must provide substantial evidence that a new drug is safe prior to receiving FDA approval, sothat the FDA can confidently certify the safety of the drug to potential consumers.(a) If the new drug testing were to be placed in a test of hypothesis framework, would the null hypothesis bethat the drug is safe or unsafe? The alternative hypothesis? (In an actual test, "safety" could be quantified usingpopulation parameters; Problem 7 is a conceptual exercise.) Fill in the blanks below.The null hypothesis would be that the drug isbe that the drug isand the alternative hypothesis would(b) Given the choice of null and alternative hypotheses in part (a), describe the Type I and Type II errors in termsof this application. Define a and B in terms of this application. Fill in the blanks below.The Type I error for this problem would be to conclude that the drug isis actuallywhen the drugThe Type II error for this problem would be to conclude that the drug iswhen the drug is actuallyIn this application a is the probability of concluding that a drugsafe when actuallyand 3 is the probability of concluding that a drugsafeitwhen the drug actuallysafe.(c) If the FDA wants to be very confident that the drug is safe before permitting it to be marketed, is it moreimportant that a or 3 be small? Circle the correct answer.(1) The value of a should be minimized to minimize the risk of falsely concluding the drug is safe when it is notsafe and could hurt people.(ii) The value of 8 should be minimized to minimize the risk of falsely concluding the drug is not safe when itis safe and could help people.(iii) The value of a should be minimized to minimize the risk of falsely concluding the drug is not safe when itis safe and could help people.(iv) The value of 3 should be minimized to minimize the risk of falsely concluding the drug is safe when it is notsafe and could hurt people.

6. Given: The number of coffee growers from Country X is n=817. The number of certified growers who…

6. In a representative sample of 817 coffee growers from Country X, 450 growers were certified to sell organic coffee markets while 62 growers were transitioning to become organic certified. In Country Y, 66% of coffee growers are organic certified. Is there evidence to indicate that fewer than 66% 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 5% chance of making a Type I error (i.e., test using a = 0.05). (a) What are the hypotheses for this test? Ho: H: (b) Calculate the value of the test statistic ze (round to two decimal places as needed): Hint: Before finding , you will first need to calculate the sample proportion p. Pay close attention to what is being tested. EITHER "certified" OR "transitioning" counts as a success for your proportion here. (c) Calculate the p-value (round to three decimal places as needed). You should find one of the following useful for part C: P(: < 0.66) 0.7454 P(: < -0.033) 0.4868 P(: < -2.01) 0.0222 P(: < -6.59) 0 (d) What is the conclusion of the test? REJECT or FAIL TO REJECT the null hypothesis because the p-value is LESS THAN or GREATER THAN the probability of making a Type I error. Therefore, there is SUFFICIENT or INSUFFICIENT evidence to indicate that fewer than 66% of the coffee growers in Country X are either organic certified or transitioning to become organic certified. (Circle the correct capitalized word or phrase in each of the three places a choice is given.) (e) If this were a two-tail test, with everything else the same, would your conclusion be different? Explain.

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P