Binomial probability distributions are used in business, science, engineering, and other fields. Suppose you work for a marketing agency and have to create a television ad for Brand A toothpaste. The toothpaste manufacturer claims that 40% of the toothpaste buyers prefer Brand A to Brand B. Your agency conducts a survey to check whether this claim is reasonable.

Respond to the following:

1.How would you do the sample survey?

◦Explain how you would conduct the survey.
◦What are the ethical implications if the manufacturer of Brand A toothpaste asked you to survey only its employees?
2.How would you interpret the outcomes?

◦After conducting a random sample of people who do not work for the manufacturer, you found that 35/100 prefer Brand A. Could the manufacturer’s claim still be true?
◦Your random sample of 100 found only 25 people who preferred Brand A. Would you still be justified in running the ad?

Binomial probability distributions are used in business, science, engineering, and other fields. Suppose you work for a marketing agency and have to create a television ad for Brand A toothpaste. The toothpaste manufacturer claims that 40% of the toothpaste buyers prefer Brand A to Brand B. Your agency conducts a survey to check whether this claim is reasonable.

Respond to the following:

1.How would you do the sample survey?
- Explain how you would conduct the survey.
- What are the ethical implications if the manufacturer of Brand A toothpaste asked you to survey only its employees?

2.How would you interpret the outcomes?
- After conducting a random sample of people who do not work for the manufacturer, you found that 35/100 prefer Brand A. Could the manufacturer's claim still be true?
- Your random sample of 100 found only 25 people who preferred Brand A. Would you still be justified in running the ad?

1. How to conduct the survey:

To conduct the survey, you would need to follow some key steps:

a. Define the target population: Determine the specific group of people you want to survey, such as toothpaste buyers.

b. Determine the sampling method: Select a suitable sampling method to ensure that your sample is representative of the target population. One common method is simple random sampling, where each member of the target population has an equal chance of being selected for the survey.

c. Determine the sample size: Decide on the number of individuals you need to include in your sample. The sample size should be large enough to ensure statistical reliability and accuracy.

d. Design the survey questionnaire: Develop a well-designed survey questionnaire that includes relevant questions for collecting data on toothpaste preferences. Consider including questions on demographics, the specific brands being compared, and reasons for preference.

e. Conduct the survey: Implement the survey by administering the questionnaire to the selected individuals. This can be done through various methods, such as face-to-face interviews, telephone interviews, online surveys, or mail surveys.

f. Analyze the data: Once you have collected the survey responses, analyze the data to determine the proportion of toothpaste buyers who prefer Brand A compared to Brand B.

Ethical implications of surveying only Brand A employees:

If the manufacturer of Brand A asks you to survey only its employees, there are several ethical implications to consider. This approach may introduce bias in the data and compromise the survey's objectivity. By excluding other toothpaste buyers from the survey, the results may not be representative of the larger population. This lack of representation can lead to misleading or inaccurate conclusions, affecting decision-making both for the manufacturer and the marketing agency. Transparency and integrity are essential in survey research to ensure unbiased results and maintain the credibility of the survey findings.

2. Interpreting the outcomes:

After conducting a random sample of people who do not work for the manufacturer, you found that 35 out of 100 prefer Brand A. Could the manufacturer's claim still be true?

To determine if the manufacturer's claim is reasonable, you can use a binomial distribution. The binomial distribution calculates the probability of a specific number of successes (individuals preferring Brand A) out of a fixed number of trials (sample size), given a specific success rate (manufacturer's claim of 40%). By calculating the probability, you can assess if the observed outcome of 35 out of 100 falls within a reasonable range based on the manufacturer's claim.

Your random sample of 100 found only 25 people who preferred Brand A. Would you still be justified in running the ad?

In this case, you may also utilize the binomial distribution to assess the probability of obtaining 25 or fewer individuals who prefer Brand A out of 100, given the manufacturer's claim of 40%. If the probability of this outcome is too low, it suggests that the observed result is significantly different from what is expected based on the manufacturer's claim. This may raise doubts about the validity of the claim and, consequently, the justification for running the ad.

It is important to consider the margin of error and other factors when interpreting survey outcomes. Additionally, consult with statistical experts or use appropriate statistical tests to draw conclusions regarding the manufacturer's claim and the justification for the advertisement.