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From the given sample of 516 people we have 235 people who like the old recipe and 281 people like the new recipe. Thus, the proportion of people who like the old recipe and the proportion of people who like the new are recipe is given by p old=0.4554 and p new= 0.5446 Thus, the proportion of people who like the old recipe less the proportion of people who like the new recipe. Hence, this is the evidence to suggest that the company should stop using the old recipe. c) Use the Four-Step-Procedure to perform a significant test at alpha value: 0.05. State: We want to perform a significant test with the hypothesis Но: р-0.5 На: р>0.5 Plan: Randomization Condition: 516 people were randomly selected for the taste test 10% Condition: 235 of the people in the sample like the old recipe Success/Failure Condition: Success: np=516(0.5)=258>10 Failure: n(1-p)=516(0.5)=258>10 Do: The test statistic is -2.0250.

From the given sample of 516 people we have 235 people who like the old recipe and 281 people like the new recipe. Thus, the proportion of people who like the old recipe and the proportion of people who like the new are recipe is given by p old=0.4554 and p new= 0.5446 Thus, the proportion of people who like the old recipe less the proportion of people who like the new recipe. Hence, this is the evidence to suggest that the company should stop using the old recipe. c) Use the Four-Step-Procedure to perform a significant test at alpha value: 0.05. State: We want to perform a significant test with the hypothesis Но: р-0.5 На: р>0.5 Plan: Randomization Condition: 516 people were randomly selected for the taste test 10% Condition: 235 of the people in the sample like the old recipe Success/Failure Condition: Success: np=516(0.5)=258>10 Failure: n(1-p)=516(0.5)=258>10 Do: The test statistic is -2.0250.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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I did letters A and B I just need help explaining letters C-E

Problem 2: An American popular soft drink company will continue to make the beverage with an old recipe until they have convincing evidence that less than 50% of customers like the taste. During a SuperBowl, the company used a new recipe for their drink. They randomly selected 516 people for the taste test. 235 of the people in the sample like the old recipe, the rest like the new recipe. a) In this situation, what is p, and what is p-hat? p=0.50 or 50% p-hat=235/516=0.4554 b) Is there some evidence to suggest that the company should stop using the old recipe for their beverage? Explain. From the given sample of 516 people we have 235 people who like the old recipe and 281 people like the new recipe. Thus, the proportion of people who like the old recipe and the proportion of people who like the new are recipe is given by p old=0.4554 and p new= 0.5446 Thus, the proportion of people who like the old recipe less the proportion of people who like the new recipe. Hence, this is the evidence to suggest that the company should stop using the old recipe. c) Use the Four-Step-Procedure to perform a significant test at alpha value: 0.05. State: We want to perform a significant test with the hypothesis Но: р-0.5 На: р>0.5 Plan: Randomization Condition: 516 people were randomly selected for the taste test 10% Condition: 235 of the people in the sample like the old recipe Success/Failure Condition: Success: np=516(0.5)=258>10 Failure: n(1-p)=516(0.5)=258>10 Do: The test statistic is -2.0250. The Z-critical value = 0.05 is 1.645. %3D Conclude: We conclude that there is evidence to claim that less than 50% of the customers like the old taste. d) Based on the conclusion in part c), what do you recommend the beverage company to do? Explain. e) What type of error would you have made in part d)? Explain. f) What is one consequence for this mistake?
Transcribed Image Text:Problem 2: An American popular soft drink company will continue to make the beverage with an old recipe until they have convincing evidence that less than 50% of customers like the taste. During a SuperBowl, the company used a new recipe for their drink. They randomly selected 516 people for the taste test. 235 of the people in the sample like the old recipe, the rest like the new recipe. a) In this situation, what is p, and what is p-hat? p=0.50 or 50% p-hat=235/516=0.4554 b) Is there some evidence to suggest that the company should stop using the old recipe for their beverage? Explain. From the given sample of 516 people we have 235 people who like the old recipe and 281 people like the new recipe. Thus, the proportion of people who like the old recipe and the proportion of people who like the new are recipe is given by p old=0.4554 and p new= 0.5446 Thus, the proportion of people who like the old recipe less the proportion of people who like the new recipe. Hence, this is the evidence to suggest that the company should stop using the old recipe. c) Use the Four-Step-Procedure to perform a significant test at alpha value: 0.05. State: We want to perform a significant test with the hypothesis Но: р-0.5 На: р>0.5 Plan: Randomization Condition: 516 people were randomly selected for the taste test 10% Condition: 235 of the people in the sample like the old recipe Success/Failure Condition: Success: np=516(0.5)=258>10 Failure: n(1-p)=516(0.5)=258>10 Do: The test statistic is -2.0250. The Z-critical value = 0.05 is 1.645. %3D Conclude: We conclude that there is evidence to claim that less than 50% of the customers like the old taste. d) Based on the conclusion in part c), what do you recommend the beverage company to do? Explain. e) What type of error would you have made in part d)? Explain. f) What is one consequence for this mistake?
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